Integrate the function frac{2x}{1 + x^2}. | vedclass

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Question

(A) Let $1 + x^2 = t$. Then,differentiating both sides with respect to $x$,we get $2x \, dx = dt$. Substituting these into the integral: $\int \frac{2

Vedclass · Accepted Answer

$\log |1 + x^2| + C$

Vedclass · Answer

(A) Let $1 + x^2 = t$. Then,differentiating both sides with respect to $x$,we get $2x \, dx = dt$. Substituting these into the integral: $\int \frac{2x}{1 + x^2} \, dx = \int \frac{1}{t} \, dt$. Integrating $\frac{1}{t}$ with respect to $t$ gives $\log |t| + C$. Substituting back $t = 1 + x^2$,we get $\log |1 + x^2| + C$. Since $1 + x^2$ is always positive for all real $x$,we can write this as $\log (1 + x^2) + C$,where $C$ is an arbitrary constant.

Integrate the function $\frac{2x}{1 + x^2}$.

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