Question 1

Integral of $$u^n$$ with respect to u, for n ≠ -1

Accepted Answer

∫u^n du = $$\frac{u^{n+1}}{n+1} + C$$

Question 2

Integral of $$\frac{1}{u}$$ with respect to u

Accepted Answer

∫(1/u) du = ln|u| + C

Question 3

Integral of $$e^u$$ with respect to u

Accepted Answer

∫e^u du = e^u + C

Question 4

Integral of $$a^u$$ with respect to u, a \u003e 0, a ≠ 1

Accepted Answer

∫a^u du = $$\frac{a^u}{\ln a} + C$$

Question 5

Integral of $$\sin u$$ with respect to u

Accepted Answer

∫sin u du = -cos u + C

Question 6

Integral of $$\cos u$$ with respect to u

Accepted Answer

∫cos u du = sin u + C

Question 7

Integral of $$\sec^2 u$$ with respect to u

Accepted Answer

∫$$sec^2 u du = tan u + C$$

Question 8

Integral of $$\csc^2 u$$ with respect to u

Accepted Answer

∫$$csc^2 u du = -cot u + C$$

Question 9

Integral of $$\sec u 	an u$$ with respect to u

Accepted Answer

∫sec u tan u du = sec u + C

Question 10

Integral of $$\csc u \cot u$$ with respect to u

Accepted Answer

∫csc u cot u du = -csc u + C

Question 11

Integral of $$	an u$$ with respect to u

Accepted Answer

∫tan u du = ln|sec u| + C

Question 12

Integral of $$\cot u$$ with respect to u

Accepted Answer

∫cot u du = ln|sin u| + C

Question 13

Integral of $$\sec u$$ with respect to u

Accepted Answer

∫sec u du = ln|sec u + tan u| + C

Question 14

Integral of $$\csc u$$ with respect to u

Accepted Answer

∫csc u du = ln|csc u - cot u| + C

Question 15

Integral of $$\sin^2 u$$ with respect to u

Accepted Answer

∫$$sin^2 u du = 1/2 u - 1/4 sin 2u + C$$

Question 16

Integral of $$\cos^2 u$$ with respect to u

Accepted Answer

∫$$cos^2 u du = 1/2 u + 1/4 sin 2u + C$$

Question 17

Integral of $$	an^2 u$$ with respect to u

Accepted Answer

∫$$tan^2 u du = tan u - u + C$$

Question 18

Integral of $$\cot^2 u$$ with respect to u

Accepted Answer

∫$$cot^2 u du = -cot u - u + C$$

Question 19

Integral of $$\sin^3 u$$ with respect to u

Accepted Answer

∫$$sin^3 u du = -1/3 (2$$ + $$sin^2 u) cos u + C$$

Question 20

Integral of $$\cos^3 u$$ with respect to u

Accepted Answer

∫$$cos^3 u du = 1/3 (2$$ + $$cos^2 u) sin u + C$$

Question 21

Integral of $$	an^3 u$$ with respect to u

Accepted Answer

∫$$tan^3 u du = 1/2$$ $$tan^2 u + ln$$|cos u| + C

Question 22

Integral of $$\cot^3 u$$ with respect to u

Accepted Answer

∫$$cot^3 u du = -1/2$$ $$cot^2 u - ln$$|sin u| + C

Question 23

Integral of $$\sec^3 u$$ with respect to u

Accepted Answer

∫$$sec^3 u du = 1/2 sec u tan u + 1/2 ln$$|sec u + tan u| + C

Question 24

Integral of $$\csc^3 u$$ with respect to u

Accepted Answer

∫$$csc^3 u du = -1/2 csc u cot u + 1/2 ln$$|csc u - cot u| + C

Basic and Trigonometric Integrals in Calculus

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