Advertisements
Advertisements
प्रश्न
` ∫ {1}/{a^2 x^2- b^2}dx`
बेरीज
Advertisements
उत्तर
\[\int\frac{dx}{a^2 x^2 - b^2} \]
\[ = \frac{1}{a^2}\int\frac{dx}{x^2 - \left( \frac{b}{a} \right)^2}\]
\[ = \frac{1}{a^2} \times \frac{1}{2\frac{b}{a}} \log \left| \frac{x - \frac{b}{a}}{x + \frac{b}{a}} \right| + C \left[ \therefore \int\frac{dx}{x^2 - a^2} = \frac{1}{2a} \log \left| \frac{x - a}{x + a} \right| + C \right]\]
` = \text{1}/{2ab} \text{ log }\| \frac{ax - b}{ax + b}| + C `
shaalaa.com
या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
APPEARS IN
संबंधित प्रश्न
\[\int\frac{1}{\sqrt{x + a} + \sqrt{x + b}} dx\]
\[\int\frac{2x + 3}{\left( x - 1 \right)^2} dx\]
\[\int \sin^2 \frac{x}{2} dx\]
\[\int\frac{e^x + 1}{e^x + x} dx\]
\[\int \tan^{3/2} x \sec^2 \text{x dx}\]
\[\int\frac{e^{m \tan^{- 1} x}}{1 + x^2} dx\]
\[\int\frac{\sec^2 \sqrt{x}}{\sqrt{x}} dx\]
\[\int\frac{x^2}{\sqrt{x - 1}} dx\]
` ∫ tan^3 x sec^2 x dx `
\[\int\frac{1}{a^2 - b^2 x^2} dx\]
\[\int\frac{e^{3x}}{4 e^{6x} - 9} dx\]
\[\int\frac{1}{\sqrt{5 x^2 - 2x}} dx\]
\[\int\frac{1}{x^{2/3} \sqrt{x^{2/3} - 4}} dx\]
\[\int\frac{x + 2}{\sqrt{x^2 + 2x - 1}} \text{ dx }\]
\[\int\frac{1}{3 + 2 \cos^2 x} \text{ dx }\]
\[\int\frac{1}{13 + 3 \cos x + 4 \sin x} dx\]
`int 1/(sin x - sqrt3 cos x) dx`
\[\int\frac{1}{1 - \tan x} \text{ dx }\]
\[\int x \text{ sin 2x dx }\]
\[\int\frac{\sin^{- 1} x}{x^2} \text{ dx }\]
\[\int e^x \left( \cot x - {cosec}^2 x \right) dx\]
\[\int e^x \left[ \sec x + \log \left( \sec x + \tan x \right) \right] dx\]
\[\int e^x \left( \frac{\sin x \cos x - 1}{\sin^2 x} \right) dx\]
\[\int\left( 2x - 5 \right) \sqrt{2 + 3x - x^2} \text{ dx }\]
\[\int\frac{x^2}{\left( x - 1 \right) \left( x - 2 \right) \left( x - 3 \right)} dx\]
\[\int\frac{5x}{\left( x + 1 \right) \left( x^2 - 4 \right)} dx\]
\[\int\frac{x^2 + x - 1}{\left( x + 1 \right)^2 \left( x + 2 \right)} dx\]
\[\int\frac{\left( x - 1 \right)^2}{x^4 + x^2 + 1} \text{ dx}\]
\[\int\frac{1}{\left( x - 1 \right) \sqrt{x + 2}} \text{ dx }\]
\[\int\frac{x}{\left( x^2 + 2x + 2 \right) \sqrt{x + 1}} \text{ dx}\]
\[\int\frac{1}{x^2 + 4x - 5} \text{ dx }\]
\[\int\frac{1}{4 \sin^2 x + 4 \sin x \cos x + 5 \cos^2 x} \text{ dx }\]
\[\int\frac{x^3}{\sqrt{x^8 + 4}} \text{ dx }\]
\[\int \sec^4 x\ dx\]
\[\int\frac{\sin^5 x}{\cos^4 x} \text{ dx }\]
\[\int \log_{10} x\ dx\]
\[\int \left( x + 1 \right)^2 e^x \text{ dx }\]
\[\int\frac{x \sin^{- 1} x}{\left( 1 - x^2 \right)^{3/2}} \text{ dx}\]
\[\int\frac{e^{m \tan^{- 1} x}}{\left( 1 + x^2 \right)^{3/2}} \text{ dx}\]
\[\int\frac{x^2}{x^2 + 7x + 10} dx\]
