Advertisements
Advertisements
प्रश्न
\[\int\left\{ x^2 + e^{\log x}+ \left( \frac{e}{2} \right)^x \right\} dx\]
बेरीज
उत्तर
`∫ ( x^2 + e^log x+ (e/2 )^x ) dx`
`= ∫ x^2dx + ∫ xdx + ∫ (e/2)^x dx `
\[ = \frac{x^3}{3} + \frac{x^2}{2} + \frac{\left( \frac{e}{2} \right)^x}{\ln \left( \frac{e}{2} \right)} + C\]
shaalaa.com
या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
APPEARS IN
संबंधित प्रश्न
\[\int\left( 3x\sqrt{x} + 4\sqrt{x} + 5 \right)dx\]
\[\int\frac{x^6 + 1}{x^2 + 1} dx\]
\[\int\frac{1}{\text{cos}^2\text{ x }\left( 1 - \text{tan x} \right)^2} dx\]
\[\int\frac{x + 1}{\sqrt{2x + 3}} dx\]
\[\int \sin^2 \frac{x}{2} dx\]
\[\int\text{sin mx }\text{cos nx dx m }\neq n\]
\[\int\frac{\text{sin} \left( x - a \right)}{\text{sin}\left( x - b \right)} dx\]
\[\int\frac{1 - \cot x}{1 + \cot x} dx\]
\[\int\frac{\tan x}{\sqrt{\cos x}} dx\]
\[\int\left( 4x + 2 \right)\sqrt{x^2 + x + 1} \text{dx}\]
\[\int\frac{\cos^5 x}{\sin x} dx\]
\[\int\frac{\left( \sin^{- 1} x \right)^3}{\sqrt{1 - x^2}} dx\]
\[\int\frac{x^2 - 1}{x^2 + 4} dx\]
\[\int\frac{1}{\sqrt{5 - 4x - 2 x^2}} dx\]
\[\int\frac{1}{\sqrt{\left( x - \alpha \right)\left( \beta - x \right)}} dx, \left( \beta > \alpha \right)\]
\[\int\frac{2x + 5}{x^2 - x - 2} \text{ dx }\]
\[\int\frac{a x^3 + bx}{x^4 + c^2} dx\]
\[\int\frac{1}{3 + 2 \sin x + \cos x} \text{ dx }\]
\[\int x^2 \cos 2x\ \text{ dx }\]
\[\int \sin^{- 1} \sqrt{x} \text{ dx }\]
\[\int \tan^{- 1} \left( \frac{3x - x^3}{1 - 3 x^2} \right) dx\]
\[\int e^x \left( \frac{1}{x^2} - \frac{2}{x^3} \right) dx\]
\[\int e^x \left[ \sec x + \log \left( \sec x + \tan x \right) \right] dx\]
\[\int e^x \frac{\left( 1 - x \right)^2}{\left( 1 + x^2 \right)^2} \text{ dx }\]
\[\int\left( x + 1 \right) \sqrt{x^2 - x + 1} \text{ dx}\]
\[\int\frac{x^2 + 6x - 8}{x^3 - 4x} dx\]
\[\int\sqrt{\cot \text{θ} d } \text{ θ}\]
\[\int\frac{x^2 - 3x + 1}{x^4 + x^2 + 1} \text{ dx }\]
\[\int\frac{x^2}{\left( x - 1 \right) \sqrt{x + 2}}\text{ dx}\]
\[\int\frac{x}{\left( x^2 + 4 \right) \sqrt{x^2 + 1}} \text{ dx }\]
Write a value of
\[\int e^{3 \text{ log x}} x^4\text{ dx}\]
\[\int\frac{2}{\left( e^x + e^{- x} \right)^2} dx\]
\[\int\frac{\cos 2x - 1}{\cos 2x + 1} dx =\]
\[\int\sqrt{\frac{1 - x}{x}} \text{ dx}\]
\[\int\frac{1}{\sec x + cosec x}\text{ dx }\]
\[\int \sec^{- 1} \sqrt{x}\ dx\]
\[\int e^{2x} \left( \frac{1 + \sin 2x}{1 + \cos 2x} \right) dx\]
\[\int\frac{1}{\left( x^2 + 2 \right) \left( x^2 + 5 \right)} \text{ dx}\]
\[\int\sqrt{\frac{1 - \sqrt{x}}{1 + \sqrt{x}}} \text{ dx}\]
