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