SOLUTION: 1. Use substitution to find ʃ x(x^2 – 4)^2 dx. 2. Find ʃ sin3 x (cos x)dx, if the limits of integration are π (upper) and 0 (lower). 3. Evaluate ʃ 5/x

Algebra ->  Absolute-value -> SOLUTION: 1. Use substitution to find ʃ x(x^2 – 4)^2 dx. 2. Find ʃ sin3 x (cos x)dx, if the limits of integration are π (upper) and 0 (lower). 3. Evaluate ʃ 5/x      Log On


   

Question 1118137: 1. Use substitution to find ʃ x(x^2 – 4)^2 dx.
2. Find ʃ sin3 x (cos x)dx, if the limits of integration are π (upper) and 0 (lower).
3. Evaluate ʃ 5/x dx if the limits of integration are e2 and 1 (lower).
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
u=x%5E2-4
du=2xdx
Substituting,

Now finish the integration.
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I'm assuming you mean the 3 as an exponent,
u=sin%28x%29
du=cos%28x%29dx
So,
int%28sin%28x%29%5E3%2Cdx%29=int%28u%5E3%2Cdu%29
Finish the integration, substitute back to x, and use the limits.
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int%285%2Fx%2Cdx%29=5int%281%2Fx%2Cdx%29=5%2Aln%28x%29%2BC
Solve using the limits of integration.