# Integration: Evaluate the Definite Integral?

## Homework Statement

Q) Evaluate The Definite Integral:

∫ (x^3) / (1 + x^4) dx

Upper Limit: 1
Lower Limit: 0

## The Attempt at a Solution

I think I'm on the right track;

u = 1 + x^4
du/dx = 4x^3
du = 4x^3 dx
1/4 du = x^3 dx

When x = 0 ; u = 1
When x = 1 ; u = 2

Therefore;

∫ (1/4 du) / u

1/4 ∫ u^-1

I'm not sure if that last step is correct; but here is where I get stuck.

Help will be appreciated. Thanks.

BTW;

Answer given is (1/4) ln 2

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danago
Gold Member
$$\int \frac{dx}{x} = ln(x) + C$$

LMAOO!!!!

Silly me.

Nevermind, I got it now.