## Answers

#### Explanation:

Let us take the subst.

Now,

Here is a third solution.

#### Explanation:

Let

so that

and

The integral becomes

# = 1/2[2/5u^(5/2)+2/3u^(1/2)] +C#

# = 1/15[3u^(5/2)+5u^(3/2)]+C#

# = 1/15 u^(3/2)[3u+5]+C#

Back-substituting gets us

# = 1/15 (x^2-1)^(3/2)[3(x^2-1)+5]+C#

# = 1/15 (x^2-1)^(3/2)(3x^2+2)+C#

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