BackBasic and Trigonometric Integrals in Calculus
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1/24BackSkip to main contentBackIntegral of \(u^n\) with respect to u, for n ≠ -1
∫u^n du = \(\frac{u^{n+1}}{n+1}\) + C Integral of \(\frac{1}{u}\) with respect to u
∫(1/u) du = ln|u| + C Integral of \(e^u\) with respect to u
∫e^u du = e^u + C Integral of \(a^u\) with respect to u, a > 0, a ≠ 1
∫a^u du = \(\frac{a^u}{\ln a}\) + C Integral of \(\sin u\) with respect to u
∫sin u du = -cos u + C Integral of \(\cos u\) with respect to u
∫cos u du = sin u + C Integral of \(\sec^2 u\) with respect to u
∫sec^2 u du = tan u + C Integral of \(\csc^2 u\) with respect to u
∫csc^2 u du = -cot u + C Integral of \(\sec u \tan u\) with respect to u
∫sec u tan u du = sec u + C Integral of \(\csc u \cot u\) with respect to u
∫csc u cot u du = -csc u + C Integral of \(\tan u\) with respect to u
∫tan u du = ln|sec u| + C Integral of \(\cot u\) with respect to u
∫cot u du = ln|sin u| + C Integral of \(\sec u\) with respect to u
∫sec u du = ln|sec u + tan u| + C Integral of \(\csc u\) with respect to u
∫csc u du = ln|csc u - cot u| + C Integral of \(\sin^2 u\) with respect to u
∫sin^2 u du = 1/2 u - 1/4 sin 2u + C Integral of \(\cos^2 u\) with respect to u
∫cos^2 u du = 1/2 u + 1/4 sin 2u + C Integral of \(\tan^2 u\) with respect to u
∫tan^2 u du = tan u - u + C Integral of \(\cot^2 u\) with respect to u
∫cot^2 u du = -cot u - u + C Integral of \(\sin^3 u\) with respect to u
∫sin^3 u du = -1/3 (2 + sin^2 u) cos u + C Integral of \(\cos^3 u\) with respect to u
∫cos^3 u du = 1/3 (2 + cos^2 u) sin u + C Integral of \(\tan^3 u\) with respect to u
∫tan^3 u du = 1/2 tan^2 u + ln|cos u| + C Integral of \(\cot^3 u\) with respect to u
∫cot^3 u du = -1/2 cot^2 u - ln|sin u| + C Integral of \(\sec^3 u\) with respect to u
∫sec^3 u du = 1/2 sec u tan u + 1/2 ln|sec u + tan u| + C Integral of \(\csc^3 u\) with respect to u
∫csc^3 u du = -1/2 csc u cot u + 1/2 ln|csc u - cot u| + C
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