Advertisements
Advertisements
प्रश्न
\[\int\frac{1}{\left( \sin^{- 1} x \right) \sqrt{1 - x^2}} \text{ dx} \]
बेरीज
Advertisements
उत्तर
\[\text{ Let I} = \int\frac{1}{\sin^{- 1} x \cdot \sqrt{1 - x^2}}dx\]
\[\text{ Putting sin}^{- 1} x = t\]
\[ \Rightarrow \frac{dx}{\sqrt{1 - x^2}} = dt\]
\[ \therefore I = \int\frac{dt}{t}\]
\[ = \text{ ln }\left| t \right| + C\]
` = \text{ ln } | sin ^-1 x| + c ( ∵ t = sin ^-1 x ) `
shaalaa.com
या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
APPEARS IN
संबंधित प्रश्न
\[\int\frac{\cos x}{1 - \cos x} \text{dx }or \int\frac{\cot x}{\text{cosec } {x }- \cot x} dx\]
` ∫ 1/ {1+ cos 3x} ` dx
\[\int\frac{3x + 5}{\sqrt{7x + 9}} dx\]
\[\int\frac{2 - 3x}{\sqrt{1 + 3x}} dx\]
\[\int\frac{1}{\sqrt{1 + \cos x}} dx\]
\[\int\frac{e^{m \tan^{- 1} x}}{1 + x^2} dx\]
` ∫ x {tan^{- 1} x^2}/{1 + x^4} dx`
\[\int\frac{\sec^2 \sqrt{x}}{\sqrt{x}} dx\]
\[\int \tan^3 \text{2x sec 2x dx}\]
\[\int\frac{e^{3x}}{4 e^{6x} - 9} dx\]
\[\int\frac{\sin 8x}{\sqrt{9 + \sin^4 4x}} dx\]
\[\int\frac{1}{\sqrt{\left( 1 - x^2 \right)\left\{ 9 + \left( \sin^{- 1} x \right)^2 \right\}}} dx\]
\[\int\frac{x - 1}{3 x^2 - 4x + 3} dx\]
\[\int\frac{x + 1}{\sqrt{4 + 5x - x^2}} \text{ dx }\]
\[\int\frac{x + 2}{\sqrt{x^2 + 2x - 1}} \text{ dx }\]
\[\int\sqrt{\frac{1 - x}{1 + x}} \text{ dx }\]
\[\int\frac{1}{4 \cos^2 x + 9 \sin^2 x}\text{ dx }\]
\[\int\frac{1}{1 - 2 \sin x} \text{ dx }\]
\[\int x \cos^2 x\ dx\]
\[\int\left( e^\text{log x} + \sin x \right) \text{ cos x dx }\]
\[\int x \sin x \cos 2x\ dx\]
\[\int x \cos^3 x\ dx\]
\[\int e^x \left[ \sec x + \log \left( \sec x + \tan x \right) \right] dx\]
\[\int\left( \frac{1}{\log x} - \frac{1}{\left( \log x \right)^2} \right) dx\]
\[\int\frac{3 + 4x - x^2}{\left( x + 2 \right) \left( x - 1 \right)} dx\]
\[\int\frac{1}{x^4 - 1} dx\]
\[\int\frac{1}{\left( x - 1 \right) \sqrt{x + 2}} \text{ dx }\]
If \[\int\frac{\sin^8 x - \cos^8 x}{1 - 2 \sin^2 x \cos^2 x} dx\]
\[\int\frac{x^4 + x^2 - 1}{x^2 + 1} \text{ dx}\]
\[\int\frac{1}{\left( \sin x - 2 \cos x \right) \left( 2 \sin x + \cos x \right)} \text{ dx }\]
\[\int\frac{1 + \sin x}{\sin x \left( 1 + \cos x \right)} \text{ dx }\]
\[\int\sqrt{a^2 - x^2}\text{ dx }\]
\[\int x^3 \left( \log x \right)^2\text{ dx }\]
\[\int e^{2x} \left( \frac{1 + \sin 2x}{1 + \cos 2x} \right) dx\]
\[\int\frac{\sqrt{1 - \sin x}}{1 + \cos x} e^{- x/2} \text{ dx}\]
\[\int\frac{\sin 4x - 2}{1 - \cos 4x} e^{2x} \text{ dx}\]
\[\int\frac{\cot x + \cot^3 x}{1 + \cot^3 x} \text{ dx}\]
Find : \[\int\frac{dx}{\sqrt{3 - 2x - x^2}}\] .
Find: `int (sin2x)/sqrt(9 - cos^4x) dx`
