Advertisements
Advertisements
प्रश्न
\[\int x^2 \text{ cos x dx }\]
बेरीज
Advertisements
उत्तर
\[\int x^2 \text{ cos x dx }\]
` " Taking x"^2" as the first function and cos x as the second function . " `
\[ = x^2 \int\text{ cos x dx } - \int\left\{ \frac{d}{dx}\left( x^2 \right)\int\text{ cos x dx }\right\}dx\]
\[ = x^2 \sin x - \int2x \text{ sin x dx }\]
\[ = x^2 \sin x - 2\left[ x\int\sin x - \int\left\{ \frac{d}{dx}\left( x \right)\int\text{ sin x dx }\right\}dx \right]\]
\[ = x^2 \sin x + 2x\cos x - 2\int\text{ cos x dx }\]
\[ = x^2 \sin x + 2x \cos x - 2 \sin x + C\]
shaalaa.com
या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
APPEARS IN
संबंधित प्रश्न
\[\int\left( 3x\sqrt{x} + 4\sqrt{x} + 5 \right)dx\]
\[\int\frac{\tan x}{\sec x + \tan x} dx\]
\[\int\frac{x^3 - 3 x^2 + 5x - 7 + x^2 a^x}{2 x^2} dx\]
\[\int\sqrt{\frac{1 + \cos 2x}{1 - \cos 2x}} dx\]
\[\int\frac{\text{sin} \left( x - a \right)}{\text{sin}\left( x - b \right)} dx\]
` ∫ {sin 2x} /{a cos^2 x + b sin^2 x } ` dx
\[\int\frac{\cos 4x - \cos 2x}{\sin 4x - \sin 2x} dx\]
\[\int\frac{x \sin^{- 1} x^2}{\sqrt{1 - x^4}} dx\]
\[\int2x \sec^3 \left( x^2 + 3 \right) \tan \left( x^2 + 3 \right) dx\]
\[\int\frac{\sin \left( \text{log x} \right)}{x} dx\]
\[\int 5^{5^{5^x}} 5^{5^x} 5^x dx\]
\[\int\frac{1}{\sqrt{x} + x} \text{ dx }\]
\[\int\frac{2x - 1}{\left( x - 1 \right)^2} dx\]
\[\int x \cos^3 x^2 \sin x^2 \text{ dx }\]
\[\int\frac{x^4 + 1}{x^2 + 1} dx\]
\[\int\frac{1}{1 + x - x^2} \text{ dx }\]
\[\int\frac{1}{x \left( x^6 + 1 \right)} dx\]
\[\int\frac{\cos x}{\sqrt{4 - \sin^2 x}} dx\]
\[\int\frac{x + 1}{x^2 + x + 3} dx\]
\[\int\frac{1 - 3x}{3 x^2 + 4x + 2}\text{ dx}\]
\[\int\frac{x^3 + x^2 + 2x + 1}{x^2 - x + 1}\text{ dx }\]
\[\int\frac{2x + 1}{\sqrt{x^2 + 2x - 1}}\text{ dx }\]
\[\int\frac{x}{\sqrt{x^2 + x + 1}} \text{ dx }\]
\[\int x\ {cosec}^2 \text{ x }\ \text{ dx }\]
\[\int e^\sqrt{x} \text{ dx }\]
\[\int \tan^{- 1} \left( \sqrt{x} \right) \text{dx }\]
\[\int e^x \left( \frac{\sin 4x - 4}{1 - \cos 4x} \right) dx\]
\[\int\sqrt{2x - x^2} \text{ dx}\]
\[\int\frac{1}{x \left( x^4 + 1 \right)} dx\]
\[\int\frac{x + 1}{x \left( 1 + x e^x \right)} dx\]
Evaluate the following integral:
\[\int\frac{x^2}{1 - x^4}dx\]
\[\int\frac{x^2}{\left( x - 1 \right) \sqrt{x + 2}}\text{ dx}\]
\[\int \cos^3 (3x)\ dx\]
\[\int\frac{\left( \sin^{- 1} x \right)^3}{\sqrt{1 - x^2}} \text{ dx }\]
\[\int\frac{\sin^5 x}{\cos^4 x} \text{ dx }\]
\[\int\left( 2x + 3 \right) \sqrt{4 x^2 + 5x + 6} \text{ dx}\]
\[\int \cos^{- 1} \left( 1 - 2 x^2 \right) \text{ dx }\]
\[\int\frac{1}{\left( x^2 + 2 \right) \left( x^2 + 5 \right)} \text{ dx}\]
