What is the antiderivative of $(5x)/(x^2+1)$ ?

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Answer 1 · 2018-07-23T13:01:29

$5/2\ln(x^2+1)+C$

Given that

$\int \frac{5x}{x^2+1}\ dx$

$=5/2\int \frac{2x}{x^2+1}\ dx$

$=5/2\int \frac{d(x^2+1)}{x^2+1}$

$=5/2\ln|x^2+1|+C$

$=5/2\ln(x^2+1)+C$

What is the antiderivative of (5x)/(x^2+1)(5x)/(x^2+1)?