Download App

Indefinite Integrals — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSIndefinite Integrals3 Marks
Question
Evaluate the following integrals:
$\int\frac{(\text{x}+1)\text{e}^\text{x}}{\cos^2(\text{xe}^\text{x})}\text{ dx}$
✓

Answer

$\int\frac{(\text{x}+1)\text{e}^\text{x}}{\cos^2(\text{xe}^\text{x})}\text{ dx}$
Let $\text{x}\text{e}^\text{x}=\text{t}$
$\Rightarrow\big(1.\text{e}^\text{x}+\text{x}\text{e}^\text{x}\big)=\frac{\text{dt}}{\text{dx}}$
$\Rightarrow(\text{x}+1)\text{e}^\text{x}\text{ dx}=\text{dt}$
Now, $\int\frac{(\text{x}+1)\text{e}^\text{x}}{\cos^2(\text{xe}^\text{x})}\text{ dx}$
$=\int\frac{\text{dt}}{\cos^2\text{t}}$
$=\sec^2\text{t}\text{ dt}$
$=\tan(\text{t})+\text{C}$
$=\tan\big(\text{xe}^\text{x}\big)+\text{C}$

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 "3 Marks Question" from Indefinite Integrals→Indefinite Integrals — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If $e^{x+y} - x = 0,$ prove that $\frac{\text{dy}}{\text{dx}}=\frac{1-\text{x}}{\text{x}}$
→
Evaluate : $\int_0^1 x(1-x)^n d x$; $($ where $n \in N)$
→
Find fog and gof if : $f(x) = x^2 + 2, \text{g(x)}=1-\frac{1}{1-\text{x}}$
→
Differentiate w.r.t. $x$ of $y$$
=x+\frac{1}{x+\frac{1}{x+\frac{1}{x+\ldots \ldots \infty}}}
$
→
Differentiate the following w.r.t. x:
$\frac{8^\text{x}}{\text{x}^8}$
→
Find the value of $\int \frac{1}{1-\tan x} d x$.
→
If the matric $\text{A}=\begin{bmatrix}5 & 2&\text{x} \\\text{y} & \text{z}&-3\\4&\text{t}&-7\end{bmatrix}$ is a symmetric matrix, find $x, y, z$ and $t.$
→
Find the direction cosines of the line passing through two points $(-2, 4, -5)$ and $(1, 2, 3)$.
→
$\int\frac{\text{x}^3}{\text{x}-2}\text{dx}$
→
Assume that on an average one telephone number out of 15 called between 2 P.M. and 3 P.M. on week days is busy. What is the probability that if six randomly selected telephone numbers are called, at least 3 of them will be busy?
→