Integrating the Trigonometric Functions (HSC SSCE Mathematics Advanced): Flashcards

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Integrating the Trigonometric Functions
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∫cos⁡x dx\int \cos x \, dx

sin⁡x+C\sin x + C

∫sin⁡x dx\int \sin x \, dx

−cos⁡x+C-\cos x + C

∫sec⁡2x dx\int \sec^2 x \, dx

tan⁡x+C\tan x + C

∫cos⁡(ax+b) dx\int \cos(ax + b) \, dx

1asin⁡(ax+b)+C\frac{1}{a} \sin(ax + b) + C

∫sin⁡(ax+b) dx\int \sin(ax + b) \, dx

−1acos⁡(ax+b)+C-\frac{1}{a} \cos(ax + b) + C

Definite integrals crossing asymptotes

Meaningless, not allowed

∫tan⁡x dx\int \tan x \, dx

−log⁡e∣cos⁡x∣+C-\log_e |\cos x| + C

∫cot⁡x dx\int \cot x \, dx

log⁡e∣sin⁡x∣+C\log_e |\sin x| + C

∫u′u dx\int \frac{u'}{u} \, dx

log⁡e∣u∣+C\log_e |u| + C

∫undudx dx\int u^n \frac{du}{dx} \, dx

un+1n+1+C\frac{u^{n+1}}{n+1} + C

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