|BSM

Questions

1 / 10

Time

Score

Calculate the antiderivative using integration by parts

calculate $\int_{ }^{ }xdx$

$x\tan\tan x-\frac{x^2}{2}+c$

$\frac{x}{2}\left(x^2+1\right)-\frac{x}{2}+c$

$\frac{x}{2}\left(x^2+1\right)+\frac{x}{2}+c$

Calculate $\int_{ }^{ }\left(\ln x\right)^2dx$

$\left(x\ln xx-2\right)+2x+c$

$\left(x\ln xx-2\right)-2x+c$

$\left(\ln xx-2\right)+2x+c$

Calculate $\int_{ }^{ }xdx$

$x\tan\tan x-\frac{x^2}{2}+c$

$xx-\frac{\ln\ln\left|x^2+1\right|}{2}+c$

$xx+\frac{\ln\ln\left|x^2+1\right|}{2}+c$

Calculate $\int_{ }^{ }\ln\left(5x+1\right)dx$

$x\ln\ln\left(5x+1\right)+\frac{\ln\left(5x+1\right)}{5}-x-\frac{1}{5}+c$

$x\ln\ln\left(2x+1\right)+\frac{\ln\left(2x+1\right)}{2}+x-\frac{1}{2}+c$

$x\ln\ln\left(2x+1\right)+\frac{\ln\left(5x+1\right)}{2}-\frac{1}{2}+c$

Calculate $\int_{ }^{ }x^2\ln xdx$

$\frac{x^3\ln x}{3}-\frac{x^3}{9}+c$

$\frac{x^3\ln x}{3}+\frac{x^3}{9}+c$

$\frac{x^3\ln x}{3}-\frac{x^3}{9}$

Calculate $\int_{ }^{ }\cos\cos\ln\ln\left(2x\right)dx$

$\frac{x\sin\sin\ln\ln\left(2x\right)}{2}-\frac{x\cos\cos\ln\ln\left(x\right)}{2}+c$

$\frac{x\sin\sin\ln\ln\left(2x\right)}{2}+\frac{x\cos\cos\ln\ln\left(2x\right)}{2}+c$

$\frac{x\sin\sin\ln\ln\left(2x\right)}{2}-\frac{x\cos\cos s\ln\ln\left(x\right)}{2}$

Calculate $\int_{ }^{ }\sin\sin\ln\ln\left(x\right)dx$

$\frac{x\sin\sin\ln\ln\left(x\right)}{2}-\frac{x\cos\cos\ln\ln\left(x\right)}{2}+c$

$\frac{x\sin\sin\ln\ln\left(x\right)}{2}+\frac{x\cos\cos\ln\ln\left(x\right)}{2}+c$

$\frac{x\sin\sin\ln\ln\left(x\right)}{2}-\frac{x\cos\cos\ln\ln\left(x\right)}{2}$

Calculate $\int_{ }^{ }xxdx$

$x\tan\tan x-\frac{x^2}{2}+c$

$x\tan\tan-\ln\ln\left|\cos\cos x\right|-\frac{x^2}{2}+c$

$x\tan\tan+\ln\ln\left|\cos\cos x\right|-\frac{x^2}{2}+c$

Calculate $\int_{ }^{ }e^xx^3dx$

$x^3e^x-3\left(x^2e^x-2\left(xe^x-e^x\right)\right)+c$

$x^3e^x+3\left(x^2e^x-2\left(xe^x-e^x\right)\right)+c$

$x^3e^x-3\left(x^2e^x-\left(xe^x-e^x\right)\right)$

Calculate $\int_{ }^{ }\ln\left(x+\sqrt{x^2+1}\right)dx$

$\left(x+\sqrt{x^2+1}\right)+\sqrt{x^2+1}+c$

$\left(x+\sqrt{x^2}+1\right)-\sqrt{x^2+1}+c$

$\ln\ln\left(x+\sqrt{x^2+1}\right)-\sqrt{x^2+1}+c$

Questions

Time

Score

Calculate the antiderivative using integration by parts

calculate﻿∫xdx\int_{ }^{ }xdx∫​xdx﻿

﻿xtan⁡tan⁡x−x22+cx\tan\tan x-\frac{x^2}{2}+cxtantanx−2x2​+c﻿

﻿x2(x2+1)−x2+c\frac{x}{2}\left(x^2+1\right)-\frac{x}{2}+c2x​(x2+1)−2x​+c﻿

﻿x2(x2+1)+x2+c\frac{x}{2}\left(x^2+1\right)+\frac{x}{2}+c2x​(x2+1)+2x​+c﻿

Calculate﻿∫(ln⁡x)2dx\int_{ }^{ }\left(\ln x\right)^2dx∫​(lnx)2dx﻿

﻿(xln⁡xx−2)+2x+c\left(x\ln xx-2\right)+2x+c(xlnxx−2)+2x+c﻿

﻿(xln⁡xx−2)−2x+c\left(x\ln xx-2\right)-2x+c(xlnxx−2)−2x+c﻿

﻿(ln⁡xx−2)+2x+c\left(\ln xx-2\right)+2x+c(lnxx−2)+2x+c﻿

Calculate﻿∫xdx\int_{ }^{ }xdx∫​xdx﻿

﻿xtan⁡tan⁡x−x22+cx\tan\tan x-\frac{x^2}{2}+cxtantanx−2x2​+c﻿

﻿xx−ln⁡ln⁡∣x2+1∣2+cxx-\frac{\ln\ln\left|x^2+1\right|}{2}+cxx−2lnln∣x2+1∣​+c﻿

﻿xx+ln⁡ln⁡∣x2+1∣2+cxx+\frac{\ln\ln\left|x^2+1\right|}{2}+cxx+2lnln∣x2+1∣​+c﻿

Calculate﻿∫ln⁡(5x+1)dx\int_{ }^{ }\ln\left(5x+1\right)dx∫​ln(5x+1)dx﻿

﻿xln⁡ln⁡(5x+1)+ln⁡(5x+1)5−x−15+cx\ln\ln\left(5x+1\right)+\frac{\ln\left(5x+1\right)}{5}-x-\frac{1}{5}+cxlnln(5x+1)+5ln(5x+1)​−x−51​+c﻿

﻿xln⁡ln⁡(2x+1)+ln⁡(2x+1)2+x−12+cx\ln\ln\left(2x+1\right)+\frac{\ln\left(2x+1\right)}{2}+x-\frac{1}{2}+cxlnln(2x+1)+2ln(2x+1)​+x−21​+c﻿

﻿xln⁡ln⁡(2x+1)+ln⁡(5x+1)2−12+cx\ln\ln\left(2x+1\right)+\frac{\ln\left(5x+1\right)}{2}-\frac{1}{2}+cxlnln(2x+1)+2ln(5x+1)​−21​+c﻿

Calculate ﻿∫x2ln⁡xdx\int_{ }^{ }x^2\ln xdx∫​x2lnxdx﻿

﻿x3ln⁡x3−x39+c\frac{x^3\ln x}{3}-\frac{x^3}{9}+c3x3lnx​−9x3​+c﻿

﻿x3ln⁡x3+x39+c\frac{x^3\ln x}{3}+\frac{x^3}{9}+c3x3lnx​+9x3​+c﻿

﻿x3ln⁡x3−x39\frac{x^3\ln x}{3}-\frac{x^3}{9}3x3lnx​−9x3​﻿

Calculate ﻿∫cos⁡cos⁡ln⁡ln⁡(2x)dx\int_{ }^{ }\cos\cos\ln\ln\left(2x\right)dx∫​coscoslnln(2x)dx﻿

﻿xsin⁡sin⁡ln⁡ln⁡(2x)2−xcos⁡cos⁡ln⁡ln⁡(x)2+c\frac{x\sin\sin\ln\ln\left(2x\right)}{2}-\frac{x\cos\cos\ln\ln\left(x\right)}{2}+c2xsinsinlnln(2x)​−2xcoscoslnln(x)​+c﻿

﻿xsin⁡sin⁡ln⁡ln⁡(2x)2+xcos⁡cos⁡ln⁡ln⁡(2x)2+c\frac{x\sin\sin\ln\ln\left(2x\right)}{2}+\frac{x\cos\cos\ln\ln\left(2x\right)}{2}+c2xsinsinlnln(2x)​+2xcoscoslnln(2x)​+c﻿

﻿xsin⁡sin⁡ln⁡ln⁡(2x)2−xcos⁡cos⁡sln⁡ln⁡(x)2\frac{x\sin\sin\ln\ln\left(2x\right)}{2}-\frac{x\cos\cos s\ln\ln\left(x\right)}{2}2xsinsinlnln(2x)​−2xcoscosslnln(x)​﻿

Calculate﻿∫sin⁡sin⁡ln⁡ln⁡(x)dx\int_{ }^{ }\sin\sin\ln\ln\left(x\right)dx∫​sinsinlnln(x)dx﻿

﻿xsin⁡sin⁡ln⁡ln⁡(x)2−xcos⁡cos⁡ln⁡ln⁡(x)2+c\frac{x\sin\sin\ln\ln\left(x\right)}{2}-\frac{x\cos\cos\ln\ln\left(x\right)}{2}+c2xsinsinlnln(x)​−2xcoscoslnln(x)​+c﻿

﻿xsin⁡sin⁡ln⁡ln⁡(x)2+xcos⁡cos⁡ln⁡ln⁡(x)2+c\frac{x\sin\sin\ln\ln\left(x\right)}{2}+\frac{x\cos\cos\ln\ln\left(x\right)}{2}+c2xsinsinlnln(x)​+2xcoscoslnln(x)​+c﻿

﻿xsin⁡sin⁡ln⁡ln⁡(x)2−xcos⁡cos⁡ln⁡ln⁡(x)2\frac{x\sin\sin\ln\ln\left(x\right)}{2}-\frac{x\cos\cos\ln\ln\left(x\right)}{2}2xsinsinlnln(x)​−2xcoscoslnln(x)​﻿

Calculate ﻿∫xxdx\int_{ }^{ }xxdx∫​xxdx﻿

﻿xtan⁡tan⁡x−x22+cx\tan\tan x-\frac{x^2}{2}+cxtantanx−2x2​+c﻿

﻿xtan⁡tan⁡−ln⁡ln⁡∣cos⁡cos⁡x∣−x22+cx\tan\tan-\ln\ln\left|\cos\cos x\right|-\frac{x^2}{2}+cxtantan−lnln∣coscosx∣−2x2​+c﻿

﻿xtan⁡tan⁡+ln⁡ln⁡∣cos⁡cos⁡x∣−x22+cx\tan\tan+\ln\ln\left|\cos\cos x\right|-\frac{x^2}{2}+cxtantan+lnln∣coscosx∣−2x2​+c﻿

Calculate﻿∫exx3dx\int_{ }^{ }e^xx^3dx∫​exx3dx﻿

﻿x3ex−3(x2ex−2(xex−ex))+cx^3e^x-3\left(x^2e^x-2\left(xe^x-e^x\right)\right)+cx3ex−3(x2ex−2(xex−ex))+c﻿

﻿x3ex+3(x2ex−2(xex−ex))+cx^3e^x+3\left(x^2e^x-2\left(xe^x-e^x\right)\right)+cx3ex+3(x2ex−2(xex−ex))+c﻿

﻿x3ex−3(x2ex−(xex−ex))x^3e^x-3\left(x^2e^x-\left(xe^x-e^x\right)\right)x3ex−3(x2ex−(xex−ex))﻿

Calculate﻿∫ln⁡(x+x2+1)dx\int_{ }^{ }\ln\left(x+\sqrt{x^2+1}\right)dx∫​ln(x+x2+1​)dx﻿

﻿(x+x2+1)+x2+1+c\left(x+\sqrt{x^2+1}\right)+\sqrt{x^2+1}+c(x+x2+1​)+x2+1​+c﻿

﻿(x+x2+1)−x2+1+c\left(x+\sqrt{x^2}+1\right)-\sqrt{x^2+1}+c(x+x2​+1)−x2+1​+c﻿

﻿ln⁡ln⁡(x+x2+1)−x2+1+c\ln\ln\left(x+\sqrt{x^2+1}\right)-\sqrt{x^2+1}+clnln(x+x2+1​)−x2+1​+c﻿

Incorrect

Great!

calculate $\int_{ }^{ }xdx$

$x\tan\tan x-\frac{x^2}{2}+c$

$\frac{x}{2}\left(x^2+1\right)-\frac{x}{2}+c$

$\frac{x}{2}\left(x^2+1\right)+\frac{x}{2}+c$

Calculate $\int_{ }^{ }\left(\ln x\right)^2dx$

$\left(x\ln xx-2\right)+2x+c$

$\left(x\ln xx-2\right)-2x+c$

$\left(\ln xx-2\right)+2x+c$

Calculate $\int_{ }^{ }xdx$

$x\tan\tan x-\frac{x^2}{2}+c$

$xx-\frac{\ln\ln\left|x^2+1\right|}{2}+c$

$xx+\frac{\ln\ln\left|x^2+1\right|}{2}+c$

Calculate $\int_{ }^{ }\ln\left(5x+1\right)dx$

$x\ln\ln\left(5x+1\right)+\frac{\ln\left(5x+1\right)}{5}-x-\frac{1}{5}+c$

$x\ln\ln\left(2x+1\right)+\frac{\ln\left(2x+1\right)}{2}+x-\frac{1}{2}+c$

$x\ln\ln\left(2x+1\right)+\frac{\ln\left(5x+1\right)}{2}-\frac{1}{2}+c$

Calculate $\int_{ }^{ }x^2\ln xdx$

$\frac{x^3\ln x}{3}-\frac{x^3}{9}+c$

$\frac{x^3\ln x}{3}+\frac{x^3}{9}+c$

$\frac{x^3\ln x}{3}-\frac{x^3}{9}$

Calculate $\int_{ }^{ }\cos\cos\ln\ln\left(2x\right)dx$

$\frac{x\sin\sin\ln\ln\left(2x\right)}{2}-\frac{x\cos\cos\ln\ln\left(x\right)}{2}+c$

$\frac{x\sin\sin\ln\ln\left(2x\right)}{2}+\frac{x\cos\cos\ln\ln\left(2x\right)}{2}+c$

$\frac{x\sin\sin\ln\ln\left(2x\right)}{2}-\frac{x\cos\cos s\ln\ln\left(x\right)}{2}$

Calculate $\int_{ }^{ }\sin\sin\ln\ln\left(x\right)dx$

$\frac{x\sin\sin\ln\ln\left(x\right)}{2}-\frac{x\cos\cos\ln\ln\left(x\right)}{2}+c$

$\frac{x\sin\sin\ln\ln\left(x\right)}{2}+\frac{x\cos\cos\ln\ln\left(x\right)}{2}+c$

$\frac{x\sin\sin\ln\ln\left(x\right)}{2}-\frac{x\cos\cos\ln\ln\left(x\right)}{2}$

Calculate $\int_{ }^{ }xxdx$

$x\tan\tan x-\frac{x^2}{2}+c$

$x\tan\tan-\ln\ln\left|\cos\cos x\right|-\frac{x^2}{2}+c$

$x\tan\tan+\ln\ln\left|\cos\cos x\right|-\frac{x^2}{2}+c$

Calculate $\int_{ }^{ }e^xx^3dx$

$x^3e^x-3\left(x^2e^x-2\left(xe^x-e^x\right)\right)+c$

$x^3e^x+3\left(x^2e^x-2\left(xe^x-e^x\right)\right)+c$

$x^3e^x-3\left(x^2e^x-\left(xe^x-e^x\right)\right)$

Calculate $\int_{ }^{ }\ln\left(x+\sqrt{x^2+1}\right)dx$

$\left(x+\sqrt{x^2+1}\right)+\sqrt{x^2+1}+c$

$\left(x+\sqrt{x^2}+1\right)-\sqrt{x^2+1}+c$

$\ln\ln\left(x+\sqrt{x^2+1}\right)-\sqrt{x^2+1}+c$