Advertisements
Advertisements
प्रश्न
\[\int\left\{ x^2 + e^{\log x}+ \left( \frac{e}{2} \right)^x \right\} dx\]
योग
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
क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
APPEARS IN
संबंधित प्रश्न
\[\int\frac{x^{- 1/3} + \sqrt{x} + 2}{\sqrt[3]{x}} dx\]
\[\int\frac{2 x^4 + 7 x^3 + 6 x^2}{x^2 + 2x} dx\]
\[\int\frac{x^2 + 3x - 1}{\left( x + 1 \right)^2} dx\]
\[\int\sqrt{1 + e^x} . e^x dx\]
\[\int x^3 \sin x^4 dx\]
\[\int \tan^3 \text{2x sec 2x dx}\]
\[\int\frac{\sin^5 x}{\cos^4 x} \text{ dx }\]
\[\ \int\ x \left( 1 - x \right)^{23} dx\]
` ∫ tan x sec^4 x dx `
\[\int \cot^5 x \text{ dx }\]
\[\int\frac{e^{3x}}{4 e^{6x} - 9} dx\]
\[\int\frac{\cos x}{\sqrt{4 + \sin^2 x}} dx\]
\[\int\frac{x + 1}{x^2 + x + 3} dx\]
\[\int\frac{x + 1}{\sqrt{4 + 5x - x^2}} \text{ dx }\]
\[\int\frac{x + 2}{\sqrt{x^2 - 1}} \text{ dx }\]
\[\int\frac{2x + 5}{\sqrt{x^2 + 2x + 5}} dx\]
\[\int\frac{4 \sin x + 5 \cos x}{5 \sin x + 4 \cos x} \text{ dx }\]
\[\int x^2 e^{- x} \text{ dx }\]
\[\int \sin^{- 1} \left( 3x - 4 x^3 \right) \text{ dx }\]
\[\int\left( x + 1 \right) \text{ log x dx }\]
\[\int\frac{x \sin^{- 1} x}{\sqrt{1 - x^2}} dx\]
\[\int \sin^{- 1} \sqrt{\frac{x}{a + x}} \text{ dx }\]
\[\int\frac{e^x}{x}\left\{ \text{ x }\left( \log x \right)^2 + 2 \log x \right\} dx\]
\[\int\left( x + 1 \right) \sqrt{x^2 - x + 1} \text{ dx}\]
\[\int\left( 4x + 1 \right) \sqrt{x^2 - x - 2} \text{ dx }\]
\[\int\frac{1}{\left( x - 1 \right) \left( x + 1 \right) \left( x + 2 \right)} dx\]
\[\int\frac{3}{\left( 1 - x \right) \left( 1 + x^2 \right)} dx\]
\[\int\frac{1}{\cos x \left( 5 - 4 \sin x \right)} dx\]
Write the anti-derivative of \[\left( 3\sqrt{x} + \frac{1}{\sqrt{x}} \right) .\]
\[\int\frac{2}{\left( e^x + e^{- x} \right)^2} dx\]
\[\int\frac{\sin^2 x}{\cos^4 x} dx =\]
\[\int\frac{1 - x^4}{1 - x} \text{ dx }\]
\[\int\frac{e^x - 1}{e^x + 1} \text{ dx}\]
\[\int\frac{1}{2 - 3 \cos 2x} \text{ dx }\]
\[\int\frac{1}{5 - 4 \sin x} \text{ dx }\]
\[\int \tan^3 x\ \sec^4 x\ dx\]
\[\int\frac{x}{x^3 - 1} \text{ dx}\]
Find : \[\int\frac{dx}{\sqrt{3 - 2x - x^2}}\] .
\[\int\frac{5 x^4 + 12 x^3 + 7 x^2}{x^2 + x} dx\]
