# Solving this definite integral using integration by parts

• songoku
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songoku
Homework Statement
Relevant Equations
Integration

Using integration by parts:
$$I_n=\left. x(1+x^2)^{-n} \right|_0^1+\int_0^{1} 2nx^2(1+x^2)^{-(n+1)}dx$$
$$I_n=2^{-n} + 2n \int_0^{1} x^2(1+x^2)^{-(n+1)}dx$$
Then how to continue?

Thanks

My first approach would be work out what In+1 is and see how they relate.

Their hint of multiplying by 1 tells me that I might need to represent 1 as a fraction where numerator = denominator.

Last edited:
songoku
Hint: ##x^2 = (x^2+1) - 1##.

vanhees71 and songoku
I understand

Thank you very much scottdave and vela

WWGD and berkeman

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