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Questions

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Calculate the antiderivatives of composed functions

Calculate $\int_{ }^{ }\frac{1}{2x+34}dx$

(ln|2x+34|)/2 + c

(ln|2x-34|)/2 + c

(ln|2x-34|)/2

Calculate $\int_{ }^{ }\frac{1}{\left(x-7\right)^2}dx$

$-\frac{1}{\left(x-7\right)^2}+c$

$\frac{1}{\left(x-7\right)^2}$

$\frac{1}{\left(x-7\right)^2}+c$

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

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

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

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

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

$\frac{x^5}{5}+\frac{2x^3}{3}+x+c$

$\frac{x^5}{5}+\frac{2x^3}{3}+x$

$\frac{x^5}{5}+\frac{2x^3}{3}+c$

Calculate $\int_{ }^{ }\sqrt{1-x^2}dx$

$\frac{x}{2}+\frac{1}{4}\sin\sin\left(2x\right)+c$

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

$\frac{x}{2}+\frac{1}{4}\sin\sin\left(2x\right)$

calculate $\int_{ }^{ }9e^{x^9}x^8dx$

$e^{x^9}$

$9e^{x^9}+c$

$e^{-x^9}+c$

Calculate $\int_{ }^{ }\frac{x}{1+x^2}dx$

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

$\frac{x^2}{2}$

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

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

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

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

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

Calculate $\int_{ }^{ }2x\ dx$

$\frac{x}{2}-\frac{\sin\sin4x}{8}+c$

$\frac{x}{2}-\frac{\sin\sin4x}{8}$

$\frac{x}{2}+\frac{\sin\sin4x}{8}+c$

calculate $\int_{ }^{ }3x\ dx$

$\frac{x}{2}-\frac{\sin\sin6x}{12}+c$

$\frac{x}{2}-\frac{\sin\sin4x}{8}$

$\frac{x}{2}+\frac{\sin\sin4x}{8}+c$

Questions

Time

Score

Calculate the antiderivatives of composed functions

Calculate﻿∫12x+34dx\int_{ }^{ }\frac{1}{2x+34}dx∫​2x+341​dx﻿

(ln|2x+34|)/2 + c

(ln|2x-34|)/2 + c

(ln|2x-34|)/2

Calculate﻿∫1(x−7)2dx\int_{ }^{ }\frac{1}{\left(x-7\right)^2}dx∫​(x−7)21​dx﻿

﻿−1(x−7)2+c-\frac{1}{\left(x-7\right)^2}+c−(x−7)21​+c﻿

﻿1(x−7)2\frac{1}{\left(x-7\right)^2}(x−7)21​﻿

﻿1(x−7)2+c\frac{1}{\left(x-7\right)^2}+c(x−7)21​+c﻿

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

﻿x55+2x33+x+c\frac{x^5}{5}+\frac{2x^3}{3}+x+c5x5​+32x3​+x+c﻿

﻿x55+2x33+x\frac{x^5}{5}+\frac{2x^3}{3}+x5x5​+32x3​+x﻿

﻿x55+2x33+c\frac{x^5}{5}+\frac{2x^3}{3}+c5x5​+32x3​+c﻿

Calculate﻿∫1−x2dx\int_{ }^{ }\sqrt{1-x^2}dx∫​1−x2​dx﻿

﻿x2+14sin⁡sin⁡(2x)+c\frac{x}{2}+\frac{1}{4}\sin\sin\left(2x\right)+c2x​+41​sinsin(2x)+c﻿

﻿x2+sin⁡sin⁡(2x)+c\frac{x}{2}+\sin\sin\left(2x\right)+c2x​+sinsin(2x)+c﻿

﻿x2+14sin⁡sin⁡(2x)\frac{x}{2}+\frac{1}{4}\sin\sin\left(2x\right)2x​+41​sinsin(2x)﻿

calculate ﻿﻿∫9ex9x8dx\int_{ }^{ }9e^{x^9}x^8dx∫​9ex9x8dx﻿

﻿ex9e^{x^9}ex9﻿

﻿9ex9+c9e^{x^9}+c9ex9+c﻿

﻿e−x9+ce^{-x^9}+ce−x9+c﻿

Calculate﻿∫x1+x2dx\int_{ }^{ }\frac{x}{1+x^2}dx∫​1+x2x​dx﻿

﻿x22+c\frac{x^2}{2}+c2x2​+c﻿

﻿x22\frac{x^2}{2}2x2​﻿

﻿−(x)22+c-\frac{\left(x\right)^2}{2}+c−2(x)2​+c﻿

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

﻿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

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

Calculate ﻿∫2x dx\int_{ }^{ }2x\ dx∫​2x dx﻿

﻿x2−sin⁡sin⁡4x8+c\frac{x}{2}-\frac{\sin\sin4x}{8}+c2x​−8sinsin4x​+c﻿

﻿x2−sin⁡sin⁡4x8\frac{x}{2}-\frac{\sin\sin4x}{8}2x​−8sinsin4x​﻿

﻿x2+sin⁡sin⁡4x8+c\frac{x}{2}+\frac{\sin\sin4x}{8}+c2x​+8sinsin4x​+c﻿

calculate ﻿∫3x dx\int_{ }^{ }3x\ dx∫​3x dx﻿

﻿x2−sin⁡sin⁡6x12+c\frac{x}{2}-\frac{\sin\sin6x}{12}+c2x​−12sinsin6x​+c﻿

﻿x2−sin⁡sin⁡4x8\frac{x}{2}-\frac{\sin\sin4x}{8}2x​−8sinsin4x​﻿

﻿x2+sin⁡sin⁡4x8+c\frac{x}{2}+\frac{\sin\sin4x}{8}+c2x​+8sinsin4x​+c﻿

Incorrect

Great!

Calculate $\int_{ }^{ }\frac{1}{2x+34}dx$

Calculate $\int_{ }^{ }\frac{1}{\left(x-7\right)^2}dx$

$-\frac{1}{\left(x-7\right)^2}+c$

$\frac{1}{\left(x-7\right)^2}$

$\frac{1}{\left(x-7\right)^2}+c$

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

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

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

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

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

$\frac{x^5}{5}+\frac{2x^3}{3}+x+c$

$\frac{x^5}{5}+\frac{2x^3}{3}+x$

$\frac{x^5}{5}+\frac{2x^3}{3}+c$

Calculate $\int_{ }^{ }\sqrt{1-x^2}dx$

$\frac{x}{2}+\frac{1}{4}\sin\sin\left(2x\right)+c$

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

$\frac{x}{2}+\frac{1}{4}\sin\sin\left(2x\right)$

calculate $\int_{ }^{ }9e^{x^9}x^8dx$

$e^{x^9}$

$9e^{x^9}+c$

$e^{-x^9}+c$

Calculate $\int_{ }^{ }\frac{x}{1+x^2}dx$

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

$\frac{x^2}{2}$

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

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

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

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

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

Calculate $\int_{ }^{ }2x\ dx$

$\frac{x}{2}-\frac{\sin\sin4x}{8}+c$

$\frac{x}{2}-\frac{\sin\sin4x}{8}$

$\frac{x}{2}+\frac{\sin\sin4x}{8}+c$

calculate $\int_{ }^{ }3x\ dx$

$\frac{x}{2}-\frac{\sin\sin6x}{12}+c$

$\frac{x}{2}-\frac{\sin\sin4x}{8}$

$\frac{x}{2}+\frac{\sin\sin4x}{8}+c$