x^n+1-x d x= Option 1: /n _e|x^n-1x^n|+C Option 2: _e|x^n+1x^n-1|+C Option 3: /n _e|x^n+1x^n|+C Option 4: _e|x^nx^n-1|+C

The answer is '/n _e|x^n-1x^n|+C'. View full solution:

Calculus > Integrals

Medium

common

$\int \dfrac{\pi}{x^{n+1}-x} d x=$

$\frac{\pi}{n} \log _{e}\left|\frac{x^{n}-1}{x^{n}}\right|+C$

$\quad \log _{e}\left|\frac{x^{n}+1}{x^{n}-1}\right|+C$

$\frac{\pi}{n} \log _{e}\left|\frac{x^{n}+1}{x^{n}}\right|+C$

$\pi \log _{e}\left|\frac{x^{n}}{x^{n}-1}\right|+C$

✅ Correct Option: 1

Related questions:

2026: 19th May Shift 2

The integral $I = \int \frac{(1+\log_e x)^3}{x} dx$ is equal to

2025: 2 June Shift 1

$\int e^{(x \log 5)}e^x dx$ , is:

Where $C$ is the constant of integration.

2022: 23 Aug Shift 1

Let $\int \frac{dx}{\left(\sqrt{x} - \sqrt{x-1}\right)^2} = \alpha u(x) + \beta v(x) + C$ , where $u(x) = x^2 - x + \left(x - \frac{1}{2}\right)\sqrt{x^2 - x}$ and $v(x) = \log\left|x - \frac{1}{2} + \sqrt{x^2 - x}\right|$ . The value of $\alpha + \beta$ is :

2025: 2 June Shift 1

The value of $\int_{-a}^a f(x)dx$ where $f(x) = \frac{7^x}{1+7^x}$ is:

2025: 13 May Shift 2

$\int_{-\frac{5}{2}}^{\frac{5}{2}} |x| dx$ is equal to

2025: 15 May Shift 2

$\int \frac{(x^4 - x)^{1/4}}{x^5} dx$ is equal to

$\int \dfrac{\pi}{x^{n+1}-x} d x=$

Keyboard Shortcuts