e^x(1+x) ^2 (x e^x ) d x is equal to - Vidyadip

Question

$\int \frac{e^x(1+x)}{\cos ^2\left(x e^x\right)} d x$ is equal to

✓

Answer

$\text {Let } I=\int \frac{e^x(1+x)}{\cos ^2\left(x e^x\right)} d x$
$\text { Put } x e^x=t$
$\Rightarrow\left(x e^x+e^x\right) d x=d t$
$\Rightarrow e^x(x+1) d x=d t$
$\therefore I=\int \frac{d t}{\cos ^2 t}=\int \sec ^2 t d t=\tan t+c=\tan \left(x e^x\right)+c$

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

If $\left[\begin{array}{lll}1 & 1 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 1\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}6 \\ 3 \\ 2\end{array}\right]$, then the value of $(2 x+y-z)$ is

In the interval (1, 2), function f(x) = 2|x - 1| + 3|x - 2| is:

Monotonically increasing.
Monotonically decreasing.
Not monotonic.
Constant.

Objective of LPP is:

The plane x + y = 0:

In which of the following, function $f(x)=x^2-4 x$ +6 is increasing :

If A and B are symmetric matrices, then ABA is:

Symmetric matrix.
Skew-symmetric matrix.
Diagonal matrix.
Scalar matrix.

$A$ and $B$ are two students. Their chances of solving a problem correctly are $\frac{1}{3}$ and $\frac{1}{4}$ respectively. If the probability of their making common error is $\frac{1}{20}$ and they obtain the same answer, then the probability of their answer to be correct is.

If $\text{f}(\text{x})=\Big(\frac{\text{x}^\text{l}}{\text{x}^\text{m}}\Big)^{\text{l}+\text{m}}\Big(\frac{\text{x}^\text{m}}{\text{x}^\text{n}}\Big)^{\text{m}+\text{n}}\Big(\frac{\text{x}^\text{n}}{\text{x}^\text{l}}\Big)^{\text{n}+1},$ the $f'(x)$ is equal to :

A vector parallel to the line of intersection of the plance $\vec{\text{r}}.(3\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}})=1$ and $\vec{\text{r}}.(\hat{\text{i}}-4\hat{\text{j}}+2\hat{\text{k}})=2$ is:

$-2\hat{\text{i}}+7\hat{\text{j}}+13\hat{\text{k}}$
$2\hat{\text{i}}+7\hat{\text{j}}-13\hat{\text{k}}$
$-2\hat{\text{i}}-7\hat{\text{j}}+13\hat{\text{k}}$
$2\hat{\text{i}}+7\hat{\text{j}}+13\hat{\text{k}}$

The differential equation satisfied by $\text{ax}^{2}+\text{by}^{2}=1$ is:

$\text{xyy}_{2}+\text{y}_{1}^{2}+\text{yy}_{1}=0$
$\text{xyy}_{2}+\text{xy}_{1}^{2}-\text{yy}_{1}=0$
$\text{xyy}_{2}+\text{xy}_{1}^{2}+\text{yy}_{1}=0$
None of these.