Advertisements
Advertisements
प्रश्न
\[\int\frac{x^5 + x^{- 2} + 2}{x^2} dx\]
बेरीज
उत्तर
\[\int\left( \frac{x^5 + x^{- 2} + 2}{x^2} \right)dx\]
\[ = \int \left( \frac{x^5}{x^2} + \frac{x^{- 2}}{x^2} + \frac{2}{x^2} \right)dx\]
\[ = \int\left( x^3 + x^{- 4} + 2 x^{- 2} \right)dx\]
\[ = \frac{x^{3 + 1}}{3 + 1} + \frac{x^{- 4 + 1}}{- 4 + 1} + 2\frac{x^{- 2 + 1}}{- 2 + 1} + C\]
\[ = \frac{x^4}{4} - \frac{1}{3 x^3} - \frac{2}{x} + C\]
shaalaa.com
या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
APPEARS IN
संबंधित प्रश्न
\[\int\left( \sec^2 x + {cosec}^2 x \right) dx\]
\[\int\frac{1}{1 - \cos x} dx\]
\[\int \cot^{- 1} \left( \frac{\sin 2x}{1 - \cos 2x} \right) dx\]
\[\int \sin^{- 1} \left( \frac{2 \tan x}{1 + \tan^2 x} \right) dx\]
\[\int\frac{1}{\sqrt{x + a} + \sqrt{x + b}} dx\]
\[\int\frac{1}{\sqrt{x + 3} - \sqrt{x + 2}} dx\]
` ∫ sin x \sqrt (1-cos 2x) dx `
\[\int\frac{e^{3x}}{e^{3x} + 1} dx\]
\[\int\frac{1 - \sin 2x}{x + \cos^2 x} dx\]
\[\int\frac{\cos^3 x}{\sqrt{\sin x}} dx\]
\[\ \int\ x \left( 1 - x \right)^{23} dx\]
\[\int\frac{1}{\sqrt{3 x^2 + 5x + 7}} dx\]
\[\int\frac{1}{\sqrt{7 - 3x - 2 x^2}} dx\]
\[\int\frac{1}{\sqrt{7 - 6x - x^2}} dx\]
\[\int\frac{x}{\sqrt{4 - x^4}} dx\]
\[\int\frac{1}{x\sqrt{4 - 9 \left( \log x \right)^2}} dx\]
\[\int\frac{x}{x^2 + 3x + 2} dx\]
\[\int\frac{x + 2}{\sqrt{x^2 - 1}} \text{ dx }\]
\[\int\frac{1}{3 + 2 \cos^2 x} \text{ dx }\]
\[\int\frac{5 \cos x + 6}{2 \cos x + \sin x + 3} \text{ dx }\]
\[\int\frac{2 \sin x + 3 \cos x}{3 \sin x + 4 \cos x} dx\]
\[\int\frac{1}{4 + 3 \tan x} dx\]
\[\int\frac{\text{ log }\left( x + 2 \right)}{\left( x + 2 \right)^2} \text{ dx }\]
\[\int \cos^3 \sqrt{x}\ dx\]
\[\int e^x \left( \frac{x - 1}{2 x^2} \right) dx\]
\[\int\frac{5 x^2 - 1}{x \left( x - 1 \right) \left( x + 1 \right)} dx\]
\[\int\frac{x^2 + 6x - 8}{x^3 - 4x} dx\]
\[\int\frac{x^2}{\left( x^2 + 1 \right) \left( 3 x^2 + 4 \right)} dx\]
\[\int\frac{x^4}{\left( x - 1 \right) \left( x^2 + 1 \right)} dx\]
Write a value of
\[\int e^{3 \text{ log x}} x^4\text{ dx}\]
\[\int\frac{\sin^2 x}{\cos^4 x} dx =\]
\[\int\sqrt{3 x^2 + 4x + 1}\text{ dx }\]
\[\int \left( x + 1 \right)^2 e^x \text{ dx }\]
\[\int \sec^{- 1} \sqrt{x}\ dx\]
\[\int \tan^{- 1} \sqrt{\frac{1 - x}{1 + x}} \text{ dx }\]
\[\int \sin^{- 1} \left( 3x - 4 x^3 \right) \text{ dx}\]
\[\int\frac{1}{1 + x + x^2 + x^3} \text{ dx }\]
\[\int\sqrt{\frac{1 - \sqrt{x}}{1 + \sqrt{x}}} \text{ dx}\]
\[\int\frac{\sin 4x - 2}{1 - \cos 4x} e^{2x} \text{ dx}\]
\[\int \sin^3 \left( 2x + 1 \right) \text{dx}\]
