Advertisements
Advertisements
प्रश्न
\[\int \cot^n {cosec}^2 \text{ x dx } , n \neq - 1\]
बेरीज
उत्तर
∫ 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
या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
APPEARS IN
संबंधित प्रश्न
\[\int\left\{ x^2 + e^{\log x}+ \left( \frac{e}{2} \right)^x \right\} dx\]
\[\int\frac{x^2 + x + 5}{3x + 2} dx\]
\[\int \cos^2 \frac{x}{2} dx\]
\[\int\sqrt{\frac{1 + \cos 2x}{1 - \cos 2x}} dx\]
\[\int\frac{1}{ x \text{log x } \text{log }\left( \text{log x }\right)} dx\]
\[\int\frac{x + 1}{x \left( x + \log x \right)} dx\]
` = ∫ root (3){ cos^2 x} sin x dx `
\[\int \sin^5\text{ x }\text{cos x dx}\]
\[\int\sqrt {e^x- 1} \text{dx}\]
\[\int\frac{1}{\sin x \cos^3 x} dx\]
\[\int\frac{x^2 - 1}{x^2 + 4} dx\]
\[\int\frac{1}{1 + x - x^2} \text{ dx }\]
` ∫ { x^2 dx}/{x^6 - a^6} dx `
\[\int\frac{x}{3 x^4 - 18 x^2 + 11} dx\]
\[\int\frac{\sec^2 x}{\sqrt{4 + \tan^2 x}} dx\]
\[\int\frac{x}{\sqrt{4 - x^4}} dx\]
\[\int\frac{x + 7}{3 x^2 + 25x + 28}\text{ dx}\]
\[\int\frac{x^2 + x + 1}{x^2 - x} dx\]
\[\int\frac{1}{5 + 7 \cos x + \sin x} dx\]
\[\int \left( \log x \right)^2 \cdot x\ dx\]
\[\int\frac{\text{ log }\left( x + 2 \right)}{\left( x + 2 \right)^2} \text{ dx }\]
\[\int \sin^{- 1} \left( \frac{2x}{1 + x^2} \right) \text{ dx }\]
\[\int\frac{\left( x \tan^{- 1} x \right)}{\left( 1 + x^2 \right)^{3/2}} \text{ dx }\]
\[\int \cos^3 \sqrt{x}\ dx\]
\[\int e^x \left( \log x + \frac{1}{x^2} \right) dx\]
\[\int\frac{5x}{\left( x + 1 \right) \left( x^2 - 4 \right)} dx\]
\[\int\frac{2x + 1}{\left( x - 2 \right) \left( x - 3 \right)} dx\]
\[\int\frac{1}{x^4 - 1} dx\]
Evaluate the following integral:
\[\int\frac{x^2}{1 - x^4}dx\]
\[\int\frac{1}{x^4 + 3 x^2 + 1} \text{ dx }\]
\[\int\frac{x^2}{\left( x - 1 \right) \sqrt{x + 2}}\text{ dx}\]
\[\int\frac{2}{\left( e^x + e^{- x} \right)^2} dx\]
\[\int\frac{1}{e^x + e^{- x}} dx\]
\[\int\frac{1}{\text{ sin} \left( x - a \right) \text{ sin } \left( x - b \right)} \text{ dx }\]
\[\int\frac{1}{1 + 2 \cos x} \text{ dx }\]
\[\int x^2 \tan^{- 1} x\ dx\]
\[\int\frac{5 x^4 + 12 x^3 + 7 x^2}{x^2 + x} dx\]
\[\int\frac{x^2 + 1}{x^2 - 5x + 6} \text{ dx }\]
\[\int\frac{x^2}{x^2 + 7x + 10} dx\]
