Integration by Parts: Solving Integrals with √(1+x^2) and x

[Chris Fernandes]

Homework Statement

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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

 

[tommyxu3]

=x * √(1+x^2) - ∫ x^2 * 1/√(1+x^2) dx

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}}.##

 

[Chris Fernandes]

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}}.##

Thank you!