# Integration by parts

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1. Jun 2, 2016

### Chris Fernandes

1. The problem statement, all variables and given/known data

2. Relevant 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

3. 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

2. Jun 2, 2016

### tommyxu3

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

3. Jun 2, 2016

Thank you!