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The integral $\int \frac{2 x+x^3}{1+x^2} dx$ is equal to: |
$\log \left(1+x^2\right)+x+C$ where C is a constant of integration $\frac{1}{2} \log \left(1+x^2\right)+x^2+C$ where C is a constant of integration $\frac{1}{2} \log \left(1+x^2\right)+\frac{1}{2} x+C$ where C is a constant of integration $\frac{1}{2} \log \left(1+x^2\right)+\frac{x^2}{2}+C$ where C is a constant of integration |
$\frac{1}{2} \log \left(1+x^2\right)+\frac{x^2}{2}+C$ where C is a constant of integration |
The correct answer is Option (4) → $\frac{1}{2} \log \left(1+x^2\right)+\frac{x^2}{2}+C$ where C is a constant of integration $\int \frac{2 x+x^3}{1+x^2} dx$ $=\int\frac{x^3+x}{x^2+1}+\frac{x}{x^2+1}dx$ $=\int x+\frac{1}{2}\frac{2x}{(x^2+1)}dx$ $=\frac{1}{2} \log \left(1+x^2\right)+\frac{x^2}{2}+C$ |
