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Rules of Integrals

Basic Rules of Integration

1. ∫0du = C

2. ∫du = u + C

3. ∫a dx = ax + C

4. ∫aƒ(x)dx = a∫ƒ(x)dx + C

5. ∫(x + v)dx = ∫x dx + ∫v dx + C

6. ∫xndx = xn+1
n + 1 		+ C, n not equal to −1

7. ∫ 1
x 		dx = ln |x| + C

8. ∫ 1
u 		u' dx = ln |u| + C

9. ∫ au du = 1
ln a 		au + C

10. ∫eu du = eu + C

11. ∫ƒ(g(x))g'(x) dx= F(g(x)) + C

12. ∫ƒ(u) du = F(u) + C


Trigonometry Rules for Integrals

1. ∫sin u du = -cos u + C

2. ∫cos u du = sin u + C

3. ∫tan u du = -ln|cos u| + C

4. ∫cot u du = ln|sin u| + C

5. ∫sec u du = ln|sec u + tan u| + C

6. ∫csc u du = -ln|csc u + cot u| + C


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