How do you integrate $int_-1^1x(1+x)^3dx$ ?

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Answer 1 · 2017-03-26T20:04:03

Do a "u" substitute

Given: $int_-1^1x(1+x)^3dx$

let $u = x + 1$ , then $du = dx and x = u -1$

Change the limits:

$a = -1 + 1$

$a = 0$

$b = 1 + 1$

$b = 2$

$int_-1^1x(1+x)^3dx = int_0^2(u-1)u^3du$

$int_-1^1x(1+x)^3dx = int_0^2u^4-u^3du$

$int_-1^1x(1+x)^3dx = u^5/5-u^4/4|_0^2$

$int_-1^1x(1+x)^3dx = 2^5/5-2^4/4$

$int_-1^1x(1+x)^3dx = 12/5$

How do you integrate int_-1^1x(1+x)^3dxint_-1^1x(1+x)^3dx?