Advertisements
Advertisements
प्रश्न
Write the anti-derivative of \[\left( 3\sqrt{x} + \frac{1}{\sqrt{x}} \right) .\]
योग
Advertisements
उत्तर
\[\int\left( 3\sqrt{x} + \frac{1}{\sqrt{x}} \right)dx = 3 \frac{x^\frac{1}{2} + 1}{\frac{1}{2} + 1} + \frac{x^{- \frac{1}{2} + 1}}{- \frac{1}{2} + 1} + c\]
\[ = 2 x^\frac{3}{2} + 2 x^\frac{1}{2} + c\]
\[ = 2\left( x^\frac{3}{2} + x^\frac{1}{2} \right) + c\]
\[\text{ Hence , the anti - derivative of }\left( 3\sqrt{x} + \frac{1}{\sqrt{x}} \right) \text{ is 2}\left( x^\frac{3}{2} + x^\frac{1}{2} \right) + c .\]
shaalaa.com
क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
APPEARS IN
संबंधित प्रश्न
\[\int\frac{1}{\sqrt{x}}\left( 1 + \frac{1}{x} \right) dx\]
\[\int\frac{\left( x + 1 \right)\left( x - 2 \right)}{\sqrt{x}} dx\]
` ∫ {cosec x} / {"cosec x "- cot x} ` dx
\[\int\frac{1}{2 - 3x} + \frac{1}{\sqrt{3x - 2}} dx\]
\[\int\frac{2 - 3x}{\sqrt{1 + 3x}} dx\]
\[\int\frac{x}{\sqrt{x + a} - \sqrt{x + b}}dx\]
\[\int\sqrt{\frac{1 + \cos 2x}{1 - \cos 2x}} dx\]
\[\int\frac{1 + \cot x}{x + \log \sin x} dx\]
\[\int\frac{\log\left( 1 + \frac{1}{x} \right)}{x \left( 1 + x \right)} dx\]
\[\int\frac{\sin 2x}{\left( a + b \cos 2x \right)^2} dx\]
\[\int\frac{x}{\sqrt{x^2 + a^2} + \sqrt{x^2 - a^2}} dx\]
\[\int\frac{\left( \sin^{- 1} x \right)^3}{\sqrt{1 - x^2}} dx\]
\[\int\frac{1}{2 x^2 - x - 1} dx\]
\[\int\frac{1}{\sqrt{16 - 6x - x^2}} dx\]
\[\int\frac{e^x}{\sqrt{16 - e^{2x}}} dx\]
\[\int\frac{\left( 3\sin x - 2 \right)\cos x}{13 - \cos^2 x - 7\sin x}dx\]
\[\int\frac{1}{2 + \sin x + \cos x} \text{ dx }\]
\[\int\frac{1}{\sin x + \sqrt{3} \cos x} \text{ dx }\]
\[\int e^x \left( \frac{1}{x^2} - \frac{2}{x^3} \right) dx\]
\[\int e^x \left( \frac{\sin 4x - 4}{1 - \cos 4x} \right) dx\]
\[\int\frac{e^x \left( x - 4 \right)}{\left( x - 2 \right)^3} \text{ dx }\]
\[\int\sqrt{2x - x^2} \text{ dx}\]
\[\int\frac{1}{x \log x \left( 2 + \log x \right)} dx\]
\[\int\frac{\cos x}{\left( 1 - \sin x \right)^3 \left( 2 + \sin x \right)} dx\]
\[\int\frac{1}{\left( x^2 + 1 \right) \left( x^2 + 2 \right)} dx\]
\[\int\frac{x^2 + 1}{x^4 + x^2 + 1} \text{ dx }\]
\[\int\frac{x^2 + 1}{x^4 + 7 x^2 + 1} 2 \text{ dx }\]
\[\int\frac{\left( x - 1 \right)^2}{x^4 + x^2 + 1} \text{ dx}\]
\[\int\frac{x^2}{\left( x - 1 \right) \sqrt{x + 2}}\text{ dx}\]
\[\int\frac{\sin x}{3 + 4 \cos^2 x} dx\]
\[\int\frac{1}{\text{ sin} \left( x - a \right) \text{ sin } \left( x - b \right)} \text{ dx }\]
\[\int\frac{1}{x^2 + 4x - 5} \text{ dx }\]
\[\int\frac{5x + 7}{\sqrt{\left( x - 5 \right) \left( x - 4 \right)}} \text{ dx }\]
\[\int\sqrt{\frac{1 - x}{x}} \text{ dx}\]
\[\int\frac{1}{2 - 3 \cos 2x} \text{ dx }\]
\[\int\sqrt{\frac{a + x}{x}}dx\]
\[ \int\left( 1 + x^2 \right) \ \cos 2x \ dx\]
\[\int\frac{1 + x^2}{\sqrt{1 - x^2}} \text{ dx }\]
