Advertisements
Advertisements
Question
\[\int\frac{\left( x + 1 \right)\left( x - 2 \right)}{\sqrt{x}} dx\]
Sum
Advertisements
Solution
\[\int\frac{\left( x + 1 \right)\left( x - 2 \right)}{\sqrt{x}}dx\]
\[ = \int \left( \frac{x^2 - 2x + x - 2}{\sqrt{x}} \right)dx\]
`=∫((x^2-x-2)/sqrt(x))dx`
\[ = \int\left( x^\frac{3}{2} - x^\frac{1}{2} - 2 x^{- \frac{1}{2}} \right)dx\]
\[ = \left[ \frac{x^\frac{3}{2} + 1}{\frac{3}{2} + 1} \right] - \left[ \frac{x^\frac{1}{2} + 1}{\frac{1}{2} + 1} \right] - 2\left[ \frac{x^{- \frac{1}{2} + 1}}{- \frac{1}{2} + 1} \right] + C\]
\[ = \frac{2}{5} x^\frac{5}{2} - \frac{2}{3} x^\frac{3}{2} - 4 x^\frac{1}{2} + C\]
shaalaa.com
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
\[\int\frac{x + 1}{x \left( x + \log x \right)} dx\]
\[\int\frac{e^{m \tan^{- 1} x}}{1 + x^2} dx\]
\[\int {cosec}^4 \text{ 3x } \text{ dx } \]
\[\int \cot^5 x \text{ dx }\]
\[\int\frac{1}{\sin^3 x \cos^5 x} dx\]
\[\int\frac{1}{\sqrt{\left( 2 - x \right)^2 + 1}} dx\]
\[\int\frac{1}{\sqrt{\left( x - \alpha \right)\left( \beta - x \right)}} dx, \left( \beta > \alpha \right)\]
\[\int\frac{\sin x}{\sqrt{4 \cos^2 x - 1}} dx\]
\[\int\frac{\sin 2x}{\sqrt{\sin^4 x + 4 \sin^2 x - 2}} dx\]
\[\int\frac{\cos x}{\sqrt{\sin^2 x - 2 \sin x - 3}} dx\]
\[\int\frac{x + 2}{2 x^2 + 6x + 5}\text{ dx }\]
\[\int\frac{x^2}{x^2 + 7x + 10} dx\]
\[\int\frac{x^2 + x + 1}{x^2 - x + 1} \text{ dx }\]
\[\int\frac{1}{\left( \sin x - 2 \cos x \right)\left( 2 \sin x + \cos x \right)} \text{ dx }\]
`int 1/(cos x - sin x)dx`
\[\int x^2 \text{ cos x dx }\]
\[\int x\ {cosec}^2 \text{ x }\ \text{ dx }\]
\[\int\frac{\text{ log }\left( x + 2 \right)}{\left( x + 2 \right)^2} \text{ dx }\]
\[\int\left( x + 1 \right) \text{ log x dx }\]
\[\int \cos^3 \sqrt{x}\ dx\]
\[\int e^x \left( \cot x + \log \sin x \right) dx\]
∴\[\int e^{2x} \left( - \sin x + 2 \cos x \right) dx\]
\[\int\sqrt{2ax - x^2} \text{ dx}\]
\[\int\left( 2x - 5 \right) \sqrt{x^2 - 4x + 3} \text{ dx }\]
\[\int\frac{x^2 + x - 1}{\left( x + 1 \right)^2 \left( x + 2 \right)} dx\]
\[\int\frac{5 x^2 + 20x + 6}{x^3 + 2 x^2 + x} dx\]
\[\int\frac{3}{\left( 1 - x \right) \left( 1 + x^2 \right)} dx\]
\[\int\frac{1}{\sin x + \sin 2x} dx\]
\[\int\frac{x^2 + 1}{x^4 + 7 x^2 + 1} 2 \text{ dx }\]
\[\int\frac{1 - x^4}{1 - x} \text{ dx }\]
\[\int\frac{1}{e^x + 1} \text{ dx }\]
\[\int\frac{x^2}{\left( x - 1 \right)^3} dx\]
\[\int\sqrt{\frac{1 - x}{x}} \text{ dx}\]
\[\int\sqrt{3 x^2 + 4x + 1}\text{ dx }\]
\[\int x\sqrt{1 + x - x^2}\text{ dx }\]
\[\int x \sec^2 2x\ dx\]
\[\int \left( x + 1 \right)^2 e^x \text{ dx }\]
\[\int \sin^{- 1} \sqrt{\frac{x}{a + x}} \text{ dx}\]
\[\int\frac{\sqrt{1 - \sin x}}{1 + \cos x} e^{- x/2} \text{ dx}\]
