Advertisements
Advertisements
प्रश्न
\[\int x e^{2x} \text{ dx }\]
योग
Advertisements
उत्तर
\[\int x e^{2x} \text{ dx }\]
` "Taking x as the first function and e"^2x " as the second function ". `
\[ = x\int e^{2x} dx - \int\left\{ \frac{d}{dx}\left( x \right)\int e^{2x} dx \right\}dx\]
\[ = \frac{x e^{2x}}{2} - \int\left( \frac{e^{2x}}{2} \right)dx\]
\[ = \frac{x}{2} e^{2x} - \frac{e^{2x}}{4} + C\]
\[ = e^{2x} \left( \frac{x}{2} - \frac{1}{4} \right) + C\]
shaalaa.com
क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
APPEARS IN
संबंधित प्रश्न
\[\int\frac{\left( x + 1 \right)\left( x - 2 \right)}{\sqrt{x}} dx\]
\[\int \left( \tan x + \cot x \right)^2 dx\]
\[\int\frac{1}{\left( 7x - 5 \right)^3} + \frac{1}{\sqrt{5x - 4}} dx\]
` ∫ 1/ {1+ cos 3x} ` dx
\[\int\frac{2 - 3x}{\sqrt{1 + 3x}} dx\]
\[\int\text{sin mx }\text{cos nx dx m }\neq n\]
\[\int\frac{\text{sin} \left( x - a \right)}{\text{sin}\left( x - b \right)} dx\]
\[\int\left( 4x + 2 \right)\sqrt{x^2 + x + 1} \text{dx}\]
` ∫ e^{m sin ^-1 x}/ \sqrt{1-x^2} ` dx
\[\int\frac{\sin \left( \tan^{- 1} x \right)}{1 + x^2} dx\]
\[\int\frac{\sin \left( \text{log x} \right)}{x} dx\]
\[\int\frac{x^2}{\sqrt{x - 1}} dx\]
\[\int\frac{x^2}{\sqrt{3x + 4}} dx\]
\[\int\frac{1}{\sqrt{x} + \sqrt[4]{x}}dx\]
` ∫ {1}/{a^2 x^2- b^2}dx`
\[\int\frac{x}{\sqrt{4 - x^4}} dx\]
\[\int\frac{\sin 2x}{\sqrt{\sin^4 x + 4 \sin^2 x - 2}} dx\]
\[\int\frac{1 - 3x}{3 x^2 + 4x + 2}\text{ dx}\]
\[\int\frac{x^2 \left( x^4 + 4 \right)}{x^2 + 4} \text{ dx }\]
\[\int\frac{x + 2}{\sqrt{x^2 + 2x - 1}} \text{ dx }\]
\[\int\frac{1}{5 + 4 \cos x} dx\]
\[\int\frac{1}{\sqrt{3} \sin x + \cos x} dx\]
\[\int\frac{4 \sin x + 5 \cos x}{5 \sin x + 4 \cos x} \text{ dx }\]
\[\int \tan^{- 1} \left( \sqrt{x} \right) \text{dx }\]
\[\int\frac{x^3 \sin^{- 1} x^2}{\sqrt{1 - x^4}} \text{ dx }\]
\[\int\sqrt{3 - x^2} \text{ dx}\]
\[\int\frac{5 x^2 + 20x + 6}{x^3 + 2 x^2 + x} dx\]
Find \[\int\frac{2x}{\left( x^2 + 1 \right) \left( x^2 + 2 \right)^2}dx\]
Evaluate the following integral:
\[\int\frac{x^2}{\left( x^2 + a^2 \right)\left( x^2 + b^2 \right)}dx\]
\[\int\frac{x^4}{\left( x - 1 \right) \left( x^2 + 1 \right)} dx\]
\[\int x^{\sin x} \left( \frac{\sin x}{x} + \cos x . \log x \right) dx\] is equal to
\[\int \text{cosec}^2 x \text{ cos}^2 \text{ 2x dx} \]
\[\int\frac{1}{e^x + 1} \text{ dx }\]
\[\int\frac{1}{\sec x + cosec x}\text{ dx }\]
\[\int\left( 2x + 3 \right) \sqrt{4 x^2 + 5x + 6} \text{ dx}\]
\[\int\frac{1}{x\sqrt{1 + x^3}} \text{ dx}\]
\[\int x^2 \tan^{- 1} x\ dx\]
\[\int e^{2x} \left( \frac{1 + \sin 2x}{1 + \cos 2x} \right) dx\]
\[\int\frac{\sqrt{1 - \sin x}}{1 + \cos x} e^{- x/2} \text{ dx}\]
\[\int\frac{x^2}{x^2 + 7x + 10}\text{ dx }\]
