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

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Answer 1 · 2016-09-21T18:12:25

$1/2ln(x^2+1)+C, or, ln (x^2+1)^(1/2)+C, or, lnsqrt(x^2+1)+C$

Let $I=intx/(x^2+1)dx$ .

Subst. $(x^2+1)=t rArr 2xdx=dt rArr xdx=dt/2$ .

$:. I=int1/t*dt/2=1/2int1/tdt=1/2ln|t|$

$:. I=1/2ln(x^2+1)+C, or, ln (x^2+1)^(1/2)+C, or, lnsqrt(x^2+1)+C$ .

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