Advertisements
Advertisements
प्रश्न
\[\int\sqrt{x}\left( x^3 - \frac{2}{x} \right) dx\]
योग
Advertisements
उत्तर
\[\int\sqrt{x} \left( x^3 - \frac{2}{x} \right)dx\]
\[ = \int\left( x^\frac{7}{2} - \frac{2}{\sqrt{x}} \right)dx\]
\[ = \int\left( x^\frac{7}{2} - 2 x^{- \frac{1}{2}} \right) dx\]
`= x^(7/2+1) / (7/2+1) - 2 (x^(-1/2+1))/(-1/2+1 )+ C`
\[ = \frac{2}{9} x^\frac{9}{2} - 4 x^\frac{1}{2} + C\]
\[ = \frac{2}{9} x^\frac{9}{2} - 4\sqrt{x} + C\]
shaalaa.com
क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
APPEARS IN
संबंधित प्रश्न
\[\int\left( \frac{m}{x} + \frac{x}{m} + m^x + x^m + mx \right) dx\]
\[\int\left( \sec^2 x + {cosec}^2 x \right) dx\]
\[\int \tan^{- 1} \left( \frac{\sin 2x}{1 + \cos 2x} \right) dx\]
\[\int\frac{x^3 - 3 x^2 + 5x - 7 + x^2 a^x}{2 x^2} dx\]
\[\int\frac{x + 3}{\left( x + 1 \right)^4} dx\]
\[\int\frac{1}{\sqrt{2x + 3} + \sqrt{2x - 3}} dx\]
\[\int\frac{x + 1}{\sqrt{2x + 3}} dx\]
\[\int\left( 5x + 3 \right) \sqrt{2x - 1} dx\]
\[\int \cos^2 \frac{x}{2} dx\]
\[\int\frac{\cos x}{2 + 3 \sin x} dx\]
\[\int x^2 e^{x^3} \cos \left( e^{x^3} \right) dx\]
\[\int\frac{\sin\sqrt{x}}{\sqrt{x}} dx\]
\[\int\frac{2x - 1}{\left( x - 1 \right)^2} dx\]
` = ∫1/{sin^3 x cos^ 2x} dx`
\[\int\frac{1}{\sqrt{a^2 - b^2 x^2}} dx\]
\[\int\frac{1}{\sqrt{5 - 4x - 2 x^2}} dx\]
\[\int\frac{\left( 1 - x^2 \right)}{x \left( 1 - 2x \right)} \text
{dx\]
\[\int\frac{x + 2}{\sqrt{x^2 - 1}} \text{ dx }\]
\[\int\frac{1}{\sin^2 x + \sin 2x} \text{ dx }\]
\[\int\frac{3 + 2 \cos x + 4 \sin x}{2 \sin x + \cos x + 3} \text{ dx }\]
\[\int\frac{\text{ log }\left( x + 2 \right)}{\left( x + 2 \right)^2} \text{ dx }\]
\[\int\cos\sqrt{x}\ dx\]
\[\int \sin^{- 1} \sqrt{x} \text{ dx }\]
\[\int x^2 \tan^{- 1} x\text{ dx }\]
\[\int e^x \left( \log x + \frac{1}{x^2} \right) dx\]
\[\int\frac{2x + 1}{\left( x + 1 \right) \left( x - 2 \right)} dx\]
\[\int\frac{5x}{\left( x + 1 \right) \left( x^2 - 4 \right)} dx\]
\[\int\frac{x^2}{\left( x - 1 \right) \left( x + 1 \right)^2} dx\]
\[\int\frac{4 x^4 + 3}{\left( x^2 + 2 \right) \left( x^2 + 3 \right) \left( x^2 + 4 \right)} dx\]
\[\int\frac{\left( x - 1 \right)^2}{x^4 + x^2 + 1} \text{ dx}\]
\[\int\frac{1}{\left( x - 1 \right) \sqrt{x^2 + 1}} \text{ dx }\]
\[\int\frac{1}{\left( 2 x^2 + 3 \right) \sqrt{x^2 - 4}} \text{ dx }\]
\[\int \sin^5 x\ dx\]
\[\int \tan^3 x\ \sec^4 x\ dx\]
\[\int\sqrt{a^2 - x^2}\text{ dx }\]
\[\int x\sqrt{\frac{1 - x}{1 + x}} \text{ dx }\]
\[\int\frac{1}{1 + x + x^2 + x^3} \text{ dx }\]
Find: `int (sin2x)/sqrt(9 - cos^4x) dx`
