Question

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

Answer 1

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

Explanation:

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`