Advertisements
Advertisements
Question
\[\int \cot^n {cosec}^2 \text{ x dx } , n \neq - 1\]
Sum
Advertisements
Solution
∫ cotn x cosec2 x dx
Let cot x = t
⇒ –cosec2 x dx = dt
⇒ cosec2 x dx = –dt
\[Now, \int \cot^n \text{ x } {cosec}^2 \text { x dx }\]
\[ = - \int t^n dt \]
\[ = \frac{- t^{n + 1}}{n + 1} + C\]
\[ = - \frac{\cot^{n + 1} x}{n + 1} + C\]
shaalaa.com
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
\[\int \left( \sqrt{x} - \frac{1}{\sqrt{x}} \right)^2 dx\]
\[\int\frac{\left( 1 + x \right)^3}{\sqrt{x}} dx\]
\[\int\left( \sec^2 x + {cosec}^2 x \right) dx\]
\[\int\frac{1 + \cos x}{1 - \cos x} dx\]
\[\int\frac{x^3}{x - 2} dx\]
\[\int \cos^2 \text{nx dx}\]
\[\int\frac{\sin 2x}{\sin 5x \sin 3x} dx\]
\[\int\frac{x}{\sqrt{x^2 + a^2} + \sqrt{x^2 - a^2}} dx\]
\[\int\frac{e^{2x}}{1 + e^x} dx\]
` = ∫1/{sin^3 x cos^ 2x} dx`
\[\int\frac{1}{\sqrt{1 + 4 x^2}} dx\]
\[\int\frac{1}{\sqrt{a^2 + b^2 x^2}} dx\]
\[\int\frac{x^2}{x^6 + a^6} dx\]
\[\int\frac{1}{x \left( x^6 + 1 \right)} dx\]
\[\int\frac{1}{\sqrt{7 - 6x - x^2}} dx\]
\[\int\frac{x}{\sqrt{x^4 + a^4}} dx\]
\[\int\frac{\sin x}{\sqrt{4 \cos^2 x - 1}} dx\]
\[\int\frac{2x + 1}{\sqrt{x^2 + 4x + 3}} \text{ dx }\]
\[\int\frac{1}{5 + 7 \cos x + \sin x} dx\]
\[\int x \text{ sin 2x dx }\]
\[\int x\ {cosec}^2 \text{ x }\ \text{ dx }\]
\[\int x \cos^2 x\ dx\]
\[\int\frac{\sin^{- 1} x}{x^2} \text{ dx }\]
\[\int x \sin^3 x\ dx\]
\[\int e^x \left( \frac{x - 1}{2 x^2} \right) dx\]
∴\[\int e^{2x} \left( - \sin x + 2 \cos x \right) dx\]
\[\int\sqrt{3 - 2x - 2 x^2} \text{ dx}\]
\[\int\frac{5 x^2 - 1}{x \left( x - 1 \right) \left( x + 1 \right)} dx\]
\[\int\frac{1}{x\left( x^n + 1 \right)} dx\]
\[\int\frac{x^2 - 3x + 1}{x^4 + x^2 + 1} \text{ dx }\]
\[\int\frac{1}{\left( x - 1 \right) \sqrt{x + 2}} \text{ dx }\]
\[\int\frac{1}{\sqrt{3 - 2x - x^2}} \text{ dx}\]
\[\int x\sqrt{1 + x - x^2}\text{ dx }\]
\[\int \left( x + 1 \right)^2 e^x \text{ dx }\]
\[\int \sin^{- 1} \sqrt{x}\ dx\]
\[\int\frac{\sqrt{1 - \sin x}}{1 + \cos x} e^{- x/2} \text{ dx}\]
\[\int\frac{x^2 + x + 1}{\left( x + 1 \right)^2 \left( x + 2 \right)} \text{ dx}\]
\[\int\frac{x^2}{x^2 + 7x + 10} dx\]
