x^2 e^ x^3 d x equals

Question

$\int x^2 e^{x^3} d x$ equals

✓

Answer

$\text {Let } I=\int x^2 e^{x^3} d x$
$\text { Put } x^3=t$
$\Rightarrow 3 x^2 d x=d t$
$\therefore I=\int e^t \frac{d t}{3}=\frac{1}{3} e^t+C=\frac{1}{3} e^{x^3}+C$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Integrals→Integrals — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Choose the correct answer from the given four options.

$\text{X}$	$1$	$2$	$3$	$4$
$\text{P}(\text{X})$	$\frac{1}{10}$	$\frac{1}{5}$	$\frac{3}{10}$	$\frac{2}{5}$

For the following probability distribution $E(X^2)$ is equal to:

→

For the multiplication of matrices as a binary operation on the set of all matrices of the form $\begin{bmatrix}\text{a}&\text{b}\\-\text{b}&\text{a}\end{bmatrix},\text{a, b}\in\text{R}$ the inverse of $\begin{bmatrix}2&3\\-3&2\end{bmatrix}$ is:

$\begin{bmatrix}-2&3\\-3&-2\end{bmatrix}$
$\begin{bmatrix}2&3\\-3&2\end{bmatrix}$
$\begin{bmatrix}\frac{2}{13}&\frac{-3}{13}\\\frac{3}{13}&\frac{2}{13}\end{bmatrix}$
$\begin{bmatrix}1&0\\0&1\end{bmatrix}$

→

$\int_{-2}^{2}|\text{x}|\text{dx}=$

→

The derivative of $\sec^{-1}\Big(\frac{1}{2\text{x}^2+1}\Big)$ w.r.t. $\sqrt{1+3\text{x}}$ at $\text{x}=\frac{-1}{3}$