Advertisements
Advertisements
प्रश्न
\[\int\frac{\cos x}{\sqrt{\sin^2 x - 2 \sin x - 3}} dx\]
बेरीज
Advertisements
उत्तर
` ∫ { cos x dx}/{\sqrt{sin^2 x - 2 sin x - 3}}`
` text{ let } \sin x = t`
` ⇒ cos x dx = dt `
`Now,∫ { cos x dx}/{\sqrt{sin^2 x - 2 sin x - 3}}`
\[ = \int\frac{dt}{\sqrt{t^2 - 2t - 3}}\]
\[ = \int\frac{dt}{\sqrt{t^2 - 2t + 1 - 1 - 3}}\]
\[ = \int\frac{dt}{\sqrt{\left( t - 1 \right)^2 - 2^2}}\]
\[ = \text{ log }\left| t - 1 + \sqrt{\left( t - 1 \right)^2 - 2^2} \right| + C\]
\[ = \text{ log }\left| t - 1 + \sqrt{t^2 - 2t - 3} \right| + C\]
\[ = \text{ log } \left| \sin x - 1 + \sqrt{\sin^2 x - 2 \sin x - 3} \right| + C\]
shaalaa.com
या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
APPEARS IN
संबंधित प्रश्न
\[\int\left( 3x\sqrt{x} + 4\sqrt{x} + 5 \right)dx\]
\[\int\frac{\left( 1 + \sqrt{x} \right)^2}{\sqrt{x}} dx\]
\[\int\frac{2 x^4 + 7 x^3 + 6 x^2}{x^2 + 2x} dx\]
\[\int\frac{1}{1 - \sin x} dx\]
\[\int\frac{x^3 - 3 x^2 + 5x - 7 + x^2 a^x}{2 x^2} dx\]
\[\int\frac{1}{1 - \sin\frac{x}{2}} dx\]
\[\int\left( x + 2 \right) \sqrt{3x + 5} \text{dx} \]
\[\int\left( 5x + 3 \right) \sqrt{2x - 1} dx\]
\[\int\frac{- \sin x + 2 \cos x}{2 \sin x + \cos x} dx\]
\[\int\frac{\left( x + 1 \right) e^x}{\sin^2 \left( \text{x e}^x \right)} dx\]
\[\int \cot^n {cosec}^2 \text{ x dx } , n \neq - 1\]
\[\int \cot^6 x \text{ dx }\]
\[\int\frac{1}{\sqrt{\left( 2 - x \right)^2 + 1}} dx\]
\[\int\frac{e^x}{\sqrt{16 - e^{2x}}} dx\]
\[\int\frac{\cos x - \sin x}{\sqrt{8 - \sin2x}}dx\]
\[\int\frac{1}{\sin^2 x + \sin 2x} \text{ dx }\]
\[\int\frac{1}{1 - 2 \sin x} \text{ dx }\]
\[\int\frac{3 + 2 \cos x + 4 \sin x}{2 \sin x + \cos x + 3} \text{ dx }\]
\[\int x^3 \cos x^2 dx\]
\[\int\left( x + 1 \right) \text{ e}^x \text{ log } \left( x e^x \right) dx\]
\[\int \tan^{- 1} \left( \frac{2x}{1 - x^2} \right) \text{ dx }\]
\[\int\left( e^\text{log x} + \sin x \right) \text{ cos x dx }\]
\[\int\left( \tan^{- 1} x^2 \right) x\ dx\]
\[\int \sin^{- 1} \sqrt{\frac{x}{a + x}} \text{ dx }\]
\[\int e^x \sec x \left( 1 + \tan x \right) dx\]
\[\int e^x \left( \log x + \frac{1}{x^2} \right) dx\]
\[\int\sqrt{2ax - x^2} \text{ dx}\]
\[\int\sqrt{2x - x^2} \text{ dx}\]
\[\int\frac{x^2 - 1}{x^4 + 1} \text{ dx }\]
\[\int\frac{1}{\left( x + 1 \right) \sqrt{x^2 + x + 1}} \text{ dx }\]
\[\int e^x \left( \frac{1 - \sin x}{1 - \cos x} \right) dx\]
\[\int \tan^3 x\ dx\]
\[\int\sqrt{\text{ cosec x} - 1} \text{ dx }\]
\[\int\frac{5x + 7}{\sqrt{\left( x - 5 \right) \left( x - 4 \right)}} \text{ dx }\]
\[\int\frac{1}{\sin^4 x + \cos^4 x} \text{ dx}\]
\[\int\frac{1}{2 + \cos x} \text{ dx }\]
\[\int \sec^6 x\ dx\]
\[\int\sqrt{3 x^2 + 4x + 1}\text{ dx }\]
\[\int\frac{\sin x + \cos x}{\sin^4 x + \cos^4 x} \text{ dx }\]
\[\int\frac{e^{m \tan^{- 1} x}}{\left( 1 + x^2 \right)^{3/2}} \text{ dx}\]
