# Integration by parts

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## Homework Equations

∫ f(x) g'(x) dx = f(x) g(x) - ∫ f '(x) g(x) dx

f(x)=√(1+x^2)
f '(x)=x * 1/√(1+x^2)

g'(x)=1
g(x)=x

## The Attempt at a Solution

∫ √(1+x^2) * 1 dx
=x * √(1+x^2) - ∫ x^2 * 1/√(1+x^2) dx

Further integration just makes the result look further from what it's supposed to look like

The latter part may help to go to your answer. You maybe can try to make it become $\frac{x^2}{\sqrt{1+x^2}}=\sqrt{1+x^2}-\frac{1}{\sqrt{1+x^2}}.$
The latter part may help to go to your answer. You maybe can try to make it become $\frac{x^2}{\sqrt{1+x^2}}=\sqrt{1+x^2}-\frac{1}{\sqrt{1+x^2}}.$