Advertisements
Advertisements
Question
\[\int x\ {cosec}^2 \text{ x }\ \text{ dx }\]
Sum
Advertisements
Solution
\[\int x\ {cosec}^2 \text{ x }\ \text{ dx }\]
` " Taking x as the first function and cosec"^2 x " as the second function " . `
\[ = x\int {cosec}^2 x\ dx - \int\left\{ \frac{d}{dx}\left( x \right)\int {cosec}^2 x\ dx \right\}dx\]
\[ = - x \text{ cot x } + \int\text{ cot x dx }\]
\[ = - x \text{ cot x }+ \text{ log }\left| \sin x \right| + c\]
shaalaa.com
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
\[\int\frac{1 - \cos 2x}{1 + \cos 2x} dx\]
\[\int\frac{\cos^2 x - \sin^2 x}{\sqrt{1} + \cos 4x} dx\]
\[\int\frac{1}{1 - \cos x} dx\]
`∫ cos ^4 2x dx `
\[\int \cos^2 \frac{x}{2} dx\]
` ∫ cos mx cos nx dx `
\[\int\frac{1}{\sqrt{1 + \cos x}} dx\]
\[\int\frac{1}{x (3 + \log x)} dx\]
\[\int\frac{e^x + 1}{e^x + x} dx\]
\[\int\frac{\sin 2x}{\sin \left( x - \frac{\pi}{6} \right) \sin \left( x + \frac{\pi}{6} \right)} dx\]
\[\int\frac{\sin \left( \text{log x} \right)}{x} dx\]
\[\int\frac{x^5}{\sqrt{1 + x^3}} dx\]
\[\int\frac{1}{x^2 \left( x^4 + 1 \right)^{3/4}} dx\]
Evaluate the following integrals:
\[\int\cos\left\{ 2 \cot^{- 1} \sqrt{\frac{1 + x}{1 - x}} \right\}dx\]
\[\int\frac{1}{a^2 - b^2 x^2} dx\]
\[\int\frac{dx}{e^x + e^{- x}}\]
\[\int\frac{1}{\sqrt{\left( 1 - x^2 \right)\left\{ 9 + \left( \sin^{- 1} x \right)^2 \right\}}} dx\]
\[\int\frac{\cos x}{\sqrt{\sin^2 x - 2 \sin x - 3}} dx\]
\[\int\frac{x}{x^2 + 3x + 2} dx\]
` ∫ {x-3} /{ x^2 + 2x - 4 } dx `
\[\int\frac{x + 2}{2 x^2 + 6x + 5}\text{ dx }\]
\[\int\frac{\left( 3\sin x - 2 \right)\cos x}{13 - \cos^2 x - 7\sin x}dx\]
\[\int\frac{x^2}{x^2 + 7x + 10} dx\]
\[\int\frac{2x + 5}{\sqrt{x^2 + 2x + 5}} dx\]
\[\int\frac{1}{1 - 2 \sin x} \text{ dx }\]
\[\int\frac{1}{2 + \sin x + \cos x} \text{ dx }\]
\[\int x \cos^2 x\ dx\]
\[\int x^2 \tan^{- 1} x\text{ dx }\]
\[\int \cos^3 \sqrt{x}\ dx\]
\[\int x \cos^3 x\ dx\]
\[\int e^x \left( \frac{1}{x^2} - \frac{2}{x^3} \right) dx\]
\[\int e^x \left( \frac{\sin 4x - 4}{1 - \cos 4x} \right) dx\]
\[\int\frac{1}{\sin^2 x + \sin 2x} \text{ dx }\]
\[\int\frac{1}{\sin^4 x + \cos^4 x} \text{ dx}\]
\[\int \log_{10} x\ dx\]
\[\int \tan^{- 1} \sqrt{x}\ dx\]
\[\int e^x \frac{\left( 1 - x \right)^2}{\left( 1 + x^2 \right)^2} \text{ dx }\]
\[\int\frac{x^2}{\left( x - 1 \right)^3 \left( x + 1 \right)} \text{ dx}\]
\[\int\frac{x^2}{x^2 + 7x + 10}\text{ dx }\]
Find: `int (sin2x)/sqrt(9 - cos^4x) dx`
