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Questions on Integration by substitution - Calculus | MATH 1411, Study notes of Calculus
Material Type: Notes; Class: Calculus II; Subject: Mathematics; University: Seton Hall University; Term: Unknown 2005;
Typology: Study notes
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Integration by subsitution
Most of the following integrals can be found by subsitution. Solve each integral by ”‘guessing”’, then verify/adjust your answer via differentiation (chain rule). For those integrals where substitution does not work, adjust the problem to enable substitution, then solve it.
- (^) ∫ (3x − 2)^4 dx
2. ∫ √
−
xdx
∫
3
√
1 −
(
− 2 x
)
dx
4. ∫
cos(x)esin(x))dx
5. ∫
xe (^34) x^3 dx
6. ∫
x sin(x^2 )ecos(x
(^2) ) dx
7. ∫
sin(x)ecos
(^2) (x) dx
8. ∫
x − 2 x^2 − 4 x + 7 dx
9. ∫
x^2 (x^3 − 1)^2 dx
10. ∫
sin(x) cos^2 (x)
dx
11. ∫
cos(x) 3
√
sin^2 (x) − 1
dx
12. ∫
ex
2
1 + ex^2
dx
13. ∫
ln(x) x
dx
∫
ln(x^2 ) x
dx
∫
x ln(x)
dx