Question:medium

The value of $ \int \frac{dx}{x(x^{n} + 1)} $ is:

Show Hint

Partial fractions are much easier to handle after a suitable substitution.

Updated On: Apr 8, 2026

$\frac{1}{n} \log \frac{x^{n}}{x^{n}+1} + c$
$\log \frac{x^{n}}{x^{n}+1} + c$
$\frac{1}{n} \log \frac{x^{n}+1}{x^{n}} + c$
None of these

Show Solution

The Correct Option is A

Solution and Explanation

Was this answer helpful?

Questions Asked in MET exam

Let $ D = \begin{vmatrix} n & n^2 & n^3 \\ n^2 & n^3 & n^5 \\ 1 & 2 & 3 \end{vmatrix} $. Then $ \lim_{n \to \infty} \frac{M_{11} + C_{33}}{(M_{13})^2} $ is:

MET - 2024
Determinants

View Solution

Given vectors $\vec{a}, \vec{b}, \vec{c}$ are non-collinear and $(\vec{a}+\vec{b})$ is collinear with $(\vec{b}+\vec{c})$ which is collinear with $\vec{a}$, and $|\vec{a}|=|\vec{b}|=|\vec{c}|=\sqrt{2}$, find $|\vec{a}+\vec{b}+\vec{c}|$.

MET - 2024
Addition of Vectors

View Solution

Given $\frac{dy}{dx} + 2y\tan x = \sin x$, $y=0$ at $x=\frac{\pi}{3}$. If maximum value of $y$ is $1/k$, find $k$.

MET - 2024
Differential equations

View Solution

A real differentiable function $f$ satisfies $f(x)+f(y)+2xy=f(x+y)$. Given $f''(0)=0$, then \[ \int_0^{\pi/2} f(\sin x)\,dx = \]

MET - 2024
Definite Integral

View Solution

The value of \( \int \frac{dx}{x(x^{n} + 1)} \) is:

Show Hint

The Correct Option is A

Solution and Explanation

Top Questions on integral

Questions Asked in MET exam