Advertisements
Advertisements
Question
\[\int\frac{x^5 + x^{- 2} + 2}{x^2} dx\]
Sum
Advertisements
Solution
\[\int\left( \frac{x^5 + x^{- 2} + 2}{x^2} \right)dx\]
\[ = \int \left( \frac{x^5}{x^2} + \frac{x^{- 2}}{x^2} + \frac{2}{x^2} \right)dx\]
\[ = \int\left( x^3 + x^{- 4} + 2 x^{- 2} \right)dx\]
\[ = \frac{x^{3 + 1}}{3 + 1} + \frac{x^{- 4 + 1}}{- 4 + 1} + 2\frac{x^{- 2 + 1}}{- 2 + 1} + C\]
\[ = \frac{x^4}{4} - \frac{1}{3 x^3} - \frac{2}{x} + C\]
shaalaa.com
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
\[\int \left( \tan x + \cot x \right)^2 dx\]
\[\int\frac{x^3 - 3 x^2 + 5x - 7 + x^2 a^x}{2 x^2} dx\]
\[\int\frac{1 + \cos x}{1 - \cos x} dx\]
\[\int\frac{a}{b + c e^x} dx\]
\[\int x^2 e^{x^3} \cos \left( e^{x^3} \right) dx\]
\[\int\frac{x}{\sqrt{x^2 + a^2} + \sqrt{x^2 - a^2}} dx\]
\[\int\frac{\sin^5 x}{\cos^4 x} \text{ dx }\]
\[\int\frac{x^2}{\sqrt{x - 1}} dx\]
\[\int\frac{2x - 1}{\left( x - 1 \right)^2} dx\]
` ∫ \sqrt{tan x} sec^4 x dx `
\[\int \cot^n {cosec}^2 \text{ x dx } , n \neq - 1\]
\[\int \cos^7 x \text{ dx } \]
\[\int \sin^3 x \cos^5 x \text{ dx }\]
\[\int\frac{1}{\sqrt{\left( x - \alpha \right)\left( \beta - x \right)}} dx, \left( \beta > \alpha \right)\]
\[\int\frac{a x^3 + bx}{x^4 + c^2} dx\]
\[\int\frac{x^2 + x - 1}{x^2 + x - 6}\text{ dx }\]
\[\int\frac{x + 2}{\sqrt{x^2 - 1}} \text{ dx }\]
\[\int\frac{5x + 3}{\sqrt{x^2 + 4x + 10}} \text{ dx }\]
\[\int\frac{1}{3 + 2 \cos^2 x} \text{ dx }\]
\[\int\frac{1}{\sin^2 x + \sin 2x} \text{ dx }\]
\[\int {cosec}^3 x\ dx\]
\[\int\frac{x^2 \tan^{- 1} x}{1 + x^2} \text{ dx }\]
\[\int \tan^{- 1} \left( \frac{2x}{1 - x^2} \right) \text{ dx }\]
\[\int e^x \left( \cot x - {cosec}^2 x \right) dx\]
\[\int\frac{5}{\left( x^2 + 1 \right) \left( x + 2 \right)} dx\]
Evaluate the following integral:
\[\int\frac{x^2}{\left( x^2 + a^2 \right)\left( x^2 + b^2 \right)}dx\]
\[\int\frac{\sin^2 x}{\cos^4 x} dx =\]
\[\int\sqrt{\frac{x}{1 - x}} dx\] is equal to
\[\int\frac{1}{\sqrt{x} + \sqrt{x + 1}} \text{ dx }\]
\[\int \cos^3 (3x)\ dx\]
\[\int\sqrt{\frac{1 - x}{x}} \text{ dx}\]
\[\int\frac{1}{2 - 3 \cos 2x} \text{ dx }\]
\[\int\frac{1}{\sec x + cosec x}\text{ dx }\]
\[\int x \sec^2 2x\ dx\]
\[\int\frac{1 + x^2}{\sqrt{1 - x^2}} \text{ dx }\]
\[\int\frac{x \sin^{- 1} x}{\left( 1 - x^2 \right)^{3/2}} \text{ dx}\]
\[\int e^{2x} \left( \frac{1 + \sin 2x}{1 + \cos 2x} \right) dx\]
\[\int\frac{\cos^7 x}{\sin x} dx\]
