d x e^ x +e^ -x is equal to - Vidyadip

Question

$\int \frac{d x}{e^{x}+e^{-x}}$ is equal to

✓

Answer

Given Integral is: $\int \frac{d x}{e^{x}+e^{-x}}$
Let $I=\int \frac{d x}{e^{x}+e^{-x}}$
$= \int \frac{d x}{e^{-x}\left(e^{2 x}+1\right)}$
$= \int \frac{e^{x} d x}{\left(e^{2 x}+1\right)}$
Put $ e^{x }= t $
$\Rightarrow e^x dx = dt$
$\Rightarrow \int \frac{\mathrm{e}^{\mathrm{x}} \mathrm{d} \mathrm{x}}{\left(\mathrm{e}^{2 \mathrm{x}}+1\right)}=\int \frac{\mathrm{dt}}{\left(\mathrm{t}^{2}+1\right)}$
$= \tan^{-1} t + C$
$= \tan^{-1} (e^x) + C$

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 "1 Marks Question" 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

Define unit vector.

Is $f: Z \rightarrow Z, f(x)=x^2$ is one-one function?

Is the measure of 10 Newton a scalar or vector?

Find the value of ${\cos ^{ - 1}}\left[ {\cos \left( {\frac{{13\pi }}{6}} \right)} \right]$

Write the position vector of the point which divides the join of points with position vectors $3\overrightarrow{\text{a}} - 2\overrightarrow{\text{b}} \text{and } 2\overrightarrow{\text{a}} + 3\overrightarrow{\text{b}}$ in the ratio $2:1.$

Write the number of vectors of unit length perpendicular to both the vectors $\overrightarrow{\text{a}} = 2\hat{\text{i}} + \hat{j} + 2\hat{\text{k}} \text{ and} \overrightarrow{\text{b}} = \hat{\text{j}} + \hat{\text{k}}.$

If $R_1$ and $R_2$ are equivalence relations in a set $A,$ show that $R_1 \cap R_2$ is also an equivalence relation.

If $\overrightarrow{\text{a}}$and$\overrightarrow{\text{b}}$ are perpendicular vectors,|$\overrightarrow{\text{a}}$+$\overrightarrow{\text{b}}$|= 13 and |$\overrightarrow{\text{a}}$| = 5 find the value of|$\overrightarrow{\text{b}}$|.

If length of three sides of a trapezium other than base are equal to $10\ cm,$ then find the area of the trapezium when it is maximum.

Classify the following measures as scalar and vector:
20kg weight.