Integrate the following functions w.r.t. x: e^ 3 z e^ 3 x +1 - Vidyadip

Question

Integrate the following functions w.r.t. x:
$\frac{e^{3 z}}{e^{3 x}+1}$

✓

Answer

Let $I=\int \frac{e^{3 x}}{e^{3 x}+1} d x$
$\text { Put } e^{3 x}+1=t$
$\therefore 3 e^{3 x} d x=d t$
$\therefore e^{3 x} d x=\frac{d t}{3}$
$\therefore I=\int \frac{1}{t} \cdot \frac{d t}{3}=\frac{1}{3} \int \frac{1}{t} d t$
$=\frac{1}{3} \log |t|+c=\frac{1}{3} \log \left|e^{3 x}+1\right|+c .$

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 "Answer the following questions in short." from Indefinite Integration→Indefinite Integration — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Diffrentiate the following w. r. t. x.

$\cos ^{-1}\left(1-x^2\right)$

Write the truth values of the following :5 is a prime number and 7 divides 94.

$|\bar{a}| \cdot(\bar{b}+\bar{c})$

State if the following is not the probability mass function of a random variable. Give reasons for your answer.

Y	−1	0	1
P(Y)	0.6	0.1	0.2

Find the general solution of $\tan 2 x=0$

In $\triangle ABC$, prove that $ac\ \cos B − bc \cos\ A = a^2 − b^2$

$\bar{a} \cdot(\bar{b} \cdot \bar{c})$

$A=\left(\begin{array}{rrr}1 & -1 & 3 \\ 2 & 1 & 0 \\ 3 & 3 & 1\end{array}\right), C_3+2 C_2$ and then $3 R_3$. What do you conclude from Ex. 5 and Ex. $6 ?$

Which of the following equations have no solutions :

$\cos ^2 \theta=-1$

Rewrite the following statements without using if .. then.If a man is a judge then he is honest.