Question
$\int \frac{ e ^{3 x}}{ e ^{3 x}+1} d x$
✓
Answer
Let $I =\int \frac{ e ^{3 x}}{ e ^{3 x}+1} d x$
Put $e ^{3 x }+1= t$
Differentiating w.r.t. $x$, we get
$ 3 e^{3 x} d x=d t$
$\therefore e^{3 x} d x=\frac{d t}{3}$
$\therefore I=\int \frac{1}{t} \cdot \frac{d t}{3}=\frac{1}{3} \log |t|+c$
$\therefore\left|\frac{1}{3} \log \right| e^{3 x}+1 \mid+c $
Put $e ^{3 x }+1= t$
Differentiating w.r.t. $x$, we get
$ 3 e^{3 x} d x=d t$
$\therefore e^{3 x} d x=\frac{d t}{3}$
$\therefore I=\int \frac{1}{t} \cdot \frac{d t}{3}=\frac{1}{3} \log |t|+c$
$\therefore\left|\frac{1}{3} \log \right| e^{3 x}+1 \mid+c $
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
If $E(X)=6$ and $\operatorname{Var}(X)=4 \cdot 2$, find $n$ and $p$.
→Evaluate: $\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} x^3 \sin ^4 x d x$
→Given an example of:
A diagonal matrix which is not scalar.
A diagonal matrix which is not scalar.
Construct a 4 × 3 matrix whose element are:
$\text{a}_\text{ij}=\frac{\text{i}-\text{j}}{\text{i}+\text{j}}$
→$\text{a}_\text{ij}=\frac{\text{i}-\text{j}}{\text{i}+\text{j}}$
It is known that error in measurement of reaction temperature (in $0^{\circ} \mathrm{C}$ ) in a certain experiment is continuous r.v. given by
$f(x)=\frac{x^2}{3}$ for $-1<x<2$
$=0$. otherwise.
Find $P(0<x \leq 1)$
→$f(x)=\frac{x^2}{3}$ for $-1<x<2$
$=0$. otherwise.
Find $P(0<x \leq 1)$
Show that the vectors $2 \hat{i}-3 \hat{j}+4 \hat{k}$ and $-4 \hat{i}+6 \hat{j}-8 \hat{k}$ are parallel.
→State which of the following are not the probability mass function of a random variable. Give reasons for your answer : 
Write the negations of the following.$Ɐ n \in N, n^2 + n + 2$ is divisible by $4$.
→Test whether the following functions are increasing or decreasing.
→$f(x)=2-3 x+3 x^2-x^3, x \in R$.
Determine the truth values ofp and q in the following cases : (p ∨ q) is T and (p ∨ q) → q is F