- #1

- 761

- 13

## Homework Statement

[tex]

1)\ \int \frac{1}{(x^2+4)^3}\ \mbox{d}x

[/tex]

[tex]

2)\ \int \frac{x}{x^4+x^2+1}\ \mbox{d}x

[/tex]

[tex]

3)\ \int \frac{x e^x}{(x+1)^2}\ \mbox{d}x

[/tex]

## The Attempt at a Solution

I got hints but I don't know how to use them.

1)

*use trigonometric substitution and double angle formulas.*

Do I have to use [tex] u=cos( \theta) [/tex] and after substituting the double angle formulas what to do next?

2)

*complete square in numerator*

But I'm missing a x^2 term!

3)

*substitute y-1 and split integrand*

Split the term?