CUET Preparation Today
Integral $\int e^x\left(1+x^2\right) d x=$ |
$e^x\left(\frac{x^3}{3}+x\right)+c$ (c is a constant) $\left(x^2+2 x\right) e^x+c$ (c is a constant) $\left(x^2-2 x+3\right) e^x+c$ (c is a constant) $2 x e^x+c$ (c is a constant) |
$\left(x^2-2 x+3\right) e^x+c$ (c is a constant) |
The correct answer is Option (3) - $\left(x^2-2 x+3\right) e^x+c$ (c is a constant) $\int e^x\left(1+x^2\right) d x$ $=\int e^xd x+\int x^2e^xdx$ $=e^x+\int x^2e^xdx$ Using DI method $⇒e^x+x^2e^x-2xe^x+2e^x+C$ $=(x^2-2x+3)e^x+C$ |
