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Antiderivative of trig functions

Calculate $\int_{ }^{ }\sin\sin\left(-13x+23\right)dx$

$\frac{\cos\cos\left(-13x+23\right)}{13}+c$

$\frac{\cos\cos\left(-13x+23\right)}{13}$

$\frac{\left(-13x+23\right)}{13}+c$

Calculate $\int_{ }^{ }24xdx$

$\frac{\tan\tan24x}{24}+c$

$\frac{\tan\tan24x}{24}$

$-\frac{\tan\tan24x}{24}+c$

Calculate $\int_{ }^{ }\cos\cos\left(8x+67\right)dx$

$\frac{\sin\sin\left(8x+67\right)}{8}+c$

$\frac{\left(8x+67\right)}{8}+c$

$\frac{\sin\sin\left(8x+67\right)}{8}$

Calculate $\int_{ }^{ }\csc\csc9x\cot\cot9xdx$

$\frac{\csc\csc9x}{9}+c$

$-\frac{\csc\csc9x}{9}+c$

$\frac{\csc\csc9x}{9}$

Calculate $\int_{ }^{ }\left(\tan\tan15x+2\right)dx$

$\frac{\ln\left|\sec\sec\left(15x+2\right)\right|}{15}+c$

$\frac{\ln\left|\csc\csc15x-2\right|}{15}+c$

$\ln\left|\sec\sec15x+2\right|+c$

Calculate $\int_{ }^{ }\tan\tan9x\sec\sec9xdx$

$\frac{\sec\sec9x}{9}+c$

$\frac{9x}{9}+c$

$-\frac{\sec\sec9x}{9}$

Calculate $\int_{ }^{ }\cot\cot\left(3x+1\right)dx$

$\frac{\ln\left|\sin\sin\left(3x+1\right)\right|}{3}+c$

$\frac{\ln\left|\sin\sin\left(x+1\right)\right|}{3}+c$

$\frac{\ln\left|\left(\sin\sin3x+1\right)\right|}{3}$

Calculate $\int_{ }^{ }\csc\csc17xdx$

$\frac{\ln\left|\csc\csc17x-\cot\cot17x\right|}{17}+c$

$\frac{\ln\left|\csc\csc17x+\cot\cot17x\right|}{17}$ +c

$\frac{\ln\left|\csc\csc17x-\cot\cot17x\right|}{17}+c$

Calculate $\int_{ }^{ }89xdx$

$\frac{\cot\cot89x}{89}+c$

$-\frac{\cot\cot89x}{89}+c$

$\frac{\cot\cot x}{89}+c$

Calculate $\int_{ }^{ }\sec\sec12xdx$

$\frac{\ln\left|\sec\sec12x+\tan\tan12x\right|}{12}+c$

$\ln\left|\sec\sec x-\tan\tan x\right|+c$

$\ln\left|\sec\sec12x+\tan\tan12x\right|$

Questions

Time

Score

Antiderivative of trig functions

Calculate﻿∫sin⁡sin⁡(−13x+23)dx\int_{ }^{ }\sin\sin\left(-13x+23\right)dx∫​sinsin(−13x+23)dx﻿

﻿cos⁡cos⁡(−13x+23)13+c\frac{\cos\cos\left(-13x+23\right)}{13}+c13coscos(−13x+23)​+c﻿

﻿cos⁡cos⁡(−13x+23)13\frac{\cos\cos\left(-13x+23\right)}{13}13coscos(−13x+23)​﻿

﻿(−13x+23)13+c\frac{\left(-13x+23\right)}{13}+c13(−13x+23)​+c﻿

Calculate﻿∫24xdx\int_{ }^{ }24xdx∫​24xdx﻿

﻿tan⁡tan⁡24x24+c\frac{\tan\tan24x}{24}+c24tantan24x​+c﻿

﻿tan⁡tan⁡24x24\frac{\tan\tan24x}{24}24tantan24x​﻿

﻿−tan⁡tan⁡24x24+c-\frac{\tan\tan24x}{24}+c−24tantan24x​+c﻿

Calculate﻿∫cos⁡cos⁡(8x+67)dx\int_{ }^{ }\cos\cos\left(8x+67\right)dx∫​coscos(8x+67)dx﻿

﻿sin⁡sin⁡(8x+67)8+c\frac{\sin\sin\left(8x+67\right)}{8}+c8sinsin(8x+67)​+c﻿

﻿(8x+67)8+c\frac{\left(8x+67\right)}{8}+c8(8x+67)​+c﻿

﻿sin⁡sin⁡(8x+67)8\frac{\sin\sin\left(8x+67\right)}{8}8sinsin(8x+67)​﻿

Calculate﻿∫csc⁡csc⁡9xcot⁡cot⁡9xdx\int_{ }^{ }\csc\csc9x\cot\cot9xdx∫​csccsc9xcotcot9xdx﻿

﻿csc⁡csc⁡9x9+c\frac{\csc\csc9x}{9}+c9csccsc9x​+c﻿

﻿−csc⁡csc⁡9x9+c-\frac{\csc\csc9x}{9}+c−9csccsc9x​+c﻿

﻿csc⁡csc⁡9x9\frac{\csc\csc9x}{9}9csccsc9x​﻿

Calculate﻿∫(tan⁡tan⁡15x+2)dx\int_{ }^{ }\left(\tan\tan15x+2\right)dx∫​(tantan15x+2)dx﻿

﻿ln⁡∣sec⁡sec⁡(15x+2)∣15+c\frac{\ln\left|\sec\sec\left(15x+2\right)\right|}{15}+c15ln∣secsec(15x+2)∣​+c﻿

﻿ln⁡∣csc⁡csc⁡15x−2∣15+c\frac{\ln\left|\csc\csc15x-2\right|}{15}+c15ln∣csccsc15x−2∣​+c﻿

﻿ln⁡∣sec⁡sec⁡15x+2∣+c\ln\left|\sec\sec15x+2\right|+cln∣secsec15x+2∣+c﻿

Calculate﻿∫tan⁡tan⁡9xsec⁡sec⁡9xdx\int_{ }^{ }\tan\tan9x\sec\sec9xdx∫​tantan9xsecsec9xdx﻿

﻿sec⁡sec⁡9x9+c\frac{\sec\sec9x}{9}+c9secsec9x​+c﻿

﻿9x9+c\frac{9x}{9}+c99x​+c﻿

﻿−sec⁡sec⁡9x9-\frac{\sec\sec9x}{9}−9secsec9x​﻿

Calculate﻿∫cot⁡cot⁡(3x+1)dx\int_{ }^{ }\cot\cot\left(3x+1\right)dx∫​cotcot(3x+1)dx﻿

﻿ln⁡∣sin⁡sin⁡(3x+1)∣3+c\frac{\ln\left|\sin\sin\left(3x+1\right)\right|}{3}+c3ln∣sinsin(3x+1)∣​+c﻿

﻿ln⁡∣sin⁡sin⁡(x+1)∣3+c\frac{\ln\left|\sin\sin\left(x+1\right)\right|}{3}+c3ln∣sinsin(x+1)∣​+c﻿

﻿ln⁡∣(sin⁡sin⁡3x+1)∣3\frac{\ln\left|\left(\sin\sin3x+1\right)\right|}{3}3ln∣(sinsin3x+1)∣​﻿

Calculate﻿∫csc⁡csc⁡17xdx\int_{ }^{ }\csc\csc17xdx∫​csccsc17xdx﻿

﻿ln⁡∣csc⁡csc⁡17x−cot⁡cot⁡17x∣17+c\frac{\ln\left|\csc\csc17x-\cot\cot17x\right|}{17}+c17ln∣csccsc17x−cotcot17x∣​+c﻿

﻿ln⁡∣csc⁡csc⁡17x+cot⁡cot⁡17x∣17\frac{\ln\left|\csc\csc17x+\cot\cot17x\right|}{17}17ln∣csccsc17x+cotcot17x∣​﻿ +c

﻿ln⁡∣csc⁡csc⁡17x−cot⁡cot⁡17x∣17+c\frac{\ln\left|\csc\csc17x-\cot\cot17x\right|}{17}+c17ln∣csccsc17x−cotcot17x∣​+c﻿

Calculate﻿∫89xdx\int_{ }^{ }89xdx∫​89xdx﻿

﻿cot⁡cot⁡89x89+c\frac{\cot\cot89x}{89}+c89cotcot89x​+c﻿

﻿−cot⁡cot⁡89x89+c-\frac{\cot\cot89x}{89}+c−89cotcot89x​+c﻿

﻿cot⁡cot⁡x89+c\frac{\cot\cot x}{89}+c89cotcotx​+c﻿

Calculate﻿∫sec⁡sec⁡12xdx\int_{ }^{ }\sec\sec12xdx∫​secsec12xdx﻿

﻿ln⁡∣sec⁡sec⁡12x+tan⁡tan⁡12x∣12+c\frac{\ln\left|\sec\sec12x+\tan\tan12x\right|}{12}+c12ln∣secsec12x+tantan12x∣​+c﻿

﻿ln⁡∣sec⁡sec⁡x−tan⁡tan⁡x∣+c\ln\left|\sec\sec x-\tan\tan x\right|+cln∣secsecx−tantanx∣+c﻿

﻿ln⁡∣sec⁡sec⁡12x+tan⁡tan⁡12x∣\ln\left|\sec\sec12x+\tan\tan12x\right|ln∣secsec12x+tantan12x∣﻿

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Calculate $\int_{ }^{ }\sin\sin\left(-13x+23\right)dx$

$\frac{\cos\cos\left(-13x+23\right)}{13}+c$

$\frac{\cos\cos\left(-13x+23\right)}{13}$

$\frac{\left(-13x+23\right)}{13}+c$

Calculate $\int_{ }^{ }24xdx$

$\frac{\tan\tan24x}{24}+c$

$\frac{\tan\tan24x}{24}$

$-\frac{\tan\tan24x}{24}+c$

Calculate $\int_{ }^{ }\cos\cos\left(8x+67\right)dx$

$\frac{\sin\sin\left(8x+67\right)}{8}+c$

$\frac{\left(8x+67\right)}{8}+c$

$\frac{\sin\sin\left(8x+67\right)}{8}$

Calculate $\int_{ }^{ }\csc\csc9x\cot\cot9xdx$

$\frac{\csc\csc9x}{9}+c$

$-\frac{\csc\csc9x}{9}+c$

$\frac{\csc\csc9x}{9}$

Calculate $\int_{ }^{ }\left(\tan\tan15x+2\right)dx$

$\frac{\ln\left|\sec\sec\left(15x+2\right)\right|}{15}+c$

$\frac{\ln\left|\csc\csc15x-2\right|}{15}+c$

$\ln\left|\sec\sec15x+2\right|+c$

Calculate $\int_{ }^{ }\tan\tan9x\sec\sec9xdx$

$\frac{\sec\sec9x}{9}+c$

$\frac{9x}{9}+c$

$-\frac{\sec\sec9x}{9}$

Calculate $\int_{ }^{ }\cot\cot\left(3x+1\right)dx$

$\frac{\ln\left|\sin\sin\left(3x+1\right)\right|}{3}+c$

$\frac{\ln\left|\sin\sin\left(x+1\right)\right|}{3}+c$

$\frac{\ln\left|\left(\sin\sin3x+1\right)\right|}{3}$

Calculate $\int_{ }^{ }\csc\csc17xdx$

$\frac{\ln\left|\csc\csc17x-\cot\cot17x\right|}{17}+c$

$\frac{\ln\left|\csc\csc17x+\cot\cot17x\right|}{17}$ +c

$\frac{\ln\left|\csc\csc17x-\cot\cot17x\right|}{17}+c$

Calculate $\int_{ }^{ }89xdx$

$\frac{\cot\cot89x}{89}+c$

$-\frac{\cot\cot89x}{89}+c$

$\frac{\cot\cot x}{89}+c$

Calculate $\int_{ }^{ }\sec\sec12xdx$

$\frac{\ln\left|\sec\sec12x+\tan\tan12x\right|}{12}+c$

$\ln\left|\sec\sec x-\tan\tan x\right|+c$

$\ln\left|\sec\sec12x+\tan\tan12x\right|$