Advertisements
Advertisements
Question
\[\int\frac{\left( x + 1 \right)\left( x - 2 \right)}{\sqrt{x}} dx\]
Sum
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
\[\int\frac{1 + \cos x}{1 - \cos x} dx\]
\[\int \tan^2 \left( 2x - 3 \right) dx\]
\[\int\frac{2x + 1}{\sqrt{3x + 2}} dx\]
` ∫ cos mx cos nx dx `
\[\int\left( 4x + 2 \right)\sqrt{x^2 + x + 1} \text{dx}\]
\[\int\frac{\sin\sqrt{x}}{\sqrt{x}} dx\]
\[\int\frac{x^2}{\sqrt{x - 1}} dx\]
\[\int \cot^5 x \text{ dx }\]
\[\int \cos^5 x \text{ dx }\]
\[\int x \cos^3 x^2 \sin x^2 \text{ dx }\]
` ∫ {1}/{a^2 x^2- b^2}dx`
\[\int\frac{x^2 + 1}{x^2 - 5x + 6} dx\]
\[\int\frac{x^2}{x^2 + 6x + 12} \text{ dx }\]
\[\int\frac{3x + 1}{\sqrt{5 - 2x - x^2}} \text{ dx }\]
\[\int\frac{1}{5 - 4 \sin x} \text{ dx }\]
\[\int\frac{1}{p + q \tan x} \text{ dx }\]
\[\int\frac{2 \tan x + 3}{3 \tan x + 4} \text{ dx }\]
\[\int x \cos x\ dx\]
\[\int x e^x \text{ dx }\]
\[\int {cosec}^3 x\ dx\]
\[\int \sin^3 \sqrt{x}\ dx\]
\[\int e^x \frac{1 + x}{\left( 2 + x \right)^2} \text{ dx }\]
\[\int\left( x + 1 \right) \sqrt{x^2 - x + 1} \text{ dx}\]
\[\int\frac{x^2 + 1}{x^2 - 1} dx\]
\[\int\frac{1}{1 + x + x^2 + x^3} dx\]
\[\int\frac{3x + 5}{x^3 - x^2 - x + 1} dx\]
\[\int\frac{1}{\sin x \left( 3 + 2 \cos x \right)} dx\]
Evaluate the following integral:
\[\int\frac{x^2}{1 - x^4}dx\]
\[\int\frac{x^2 + 9}{x^4 + 81} \text{ dx }\]
\[\int\frac{1}{x^4 + x^2 + 1} \text{ dx }\]
The value of \[\int\frac{\sin x + \cos x}{\sqrt{1 - \sin 2x}} dx\] is equal to
\[\int\frac{\cos2x - \cos2\theta}{\cos x - \cos\theta}dx\] is equal to
\[\int\frac{e^x - 1}{e^x + 1} \text{ dx}\]
\[\int \tan^5 x\ dx\]
\[\int\frac{x^2}{\left( x - 1 \right)^3} dx\]
\[\int\frac{1}{\sin^4 x + \cos^4 x} \text{ dx}\]
\[\int \tan^5 x\ \sec^3 x\ dx\]
\[\int \left( x + 1 \right)^2 e^x \text{ dx }\]
\[\int\frac{x^2 - 2}{x^5 - x} \text{ dx}\]
