Advertisements
Advertisements
प्रश्न
\[\int\frac{1 - \cos x}{1 + \cos x} dx\]
बेरीज
Advertisements
उत्तर
\[\int\left( \frac{1 - \cos x}{1 + \cos x} \right) dx\]
`= ∫ ( {2 sin ^2 x/2 }/ {2 cos ^2 x/2})` dx ` [ 1 - cos x = 2 sin ^2 x/2 & 1 + cos x = 2 cos ^2 x/2]`
\[ = \int \tan^2 \frac{x}{2} dx\]
\[ = \int\left( \sec^2 \frac{x}{2} - 1 \right) dx\]
\[ = \frac{\tan \frac{x}{2}}{\frac{1}{2}} - x + C\]
\[ = 2 \tan \frac{x}{2} - x + C\]
shaalaa.com
या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
APPEARS IN
संबंधित प्रश्न
\[\int\frac{x^5 + x^{- 2} + 2}{x^2} dx\]
\[\int\frac{2 x^4 + 7 x^3 + 6 x^2}{x^2 + 2x} dx\]
\[\int \cos^{- 1} \left( \sin x \right) dx\]
\[\int\frac{1}{2 - 3x} + \frac{1}{\sqrt{3x - 2}} dx\]
\[\int\frac{e^x + 1}{e^x + x} dx\]
` ∫ {"cosec" x }/ { log tan x/2 ` dx
\[\int\frac{x + \sqrt{x + 1}}{x + 2} dx\]
\[\int\frac{1}{\left( x + 1 \right)\left( x^2 + 2x + 2 \right)} dx\]
\[\int\frac{x^5}{\sqrt{1 + x^3}} dx\]
` ∫ tan^5 x dx `
\[\int \cos^7 x \text{ dx } \]
Evaluate the following integrals:
\[\int\frac{x^2}{\left( a^2 - x^2 \right)^{3/2}}dx\]
\[\int\frac{dx}{e^x + e^{- x}}\]
\[\int\frac{x}{\sqrt{x^4 + a^4}} dx\]
\[\int\frac{x + 1}{x^2 + x + 3} dx\]
\[\int\frac{x^3}{x^4 + x^2 + 1}dx\]
\[\int\frac{x + 1}{\sqrt{x^2 + 1}} dx\]
\[\int\frac{2x + 1}{\sqrt{x^2 + 4x + 3}} \text{ dx }\]
\[\int\frac{1}{1 + 3 \sin^2 x} \text{ dx }\]
\[\int\frac{1}{1 - \sin x + \cos x} \text{ dx }\]
\[\int\text{ log }\left( x + 1 \right) \text{ dx }\]
\[\int x^2 \text{ cos x dx }\]
\[\int x^2 \sin^2 x\ dx\]
\[\int x\left( \frac{\sec 2x - 1}{\sec 2x + 1} \right) dx\]
\[\int\frac{\sin^{- 1} x}{x^2} \text{ dx }\]
\[\int\frac{x^2 \sin^{- 1} x}{\left( 1 - x^2 \right)^{3/2}} \text{ dx }\]
\[\int e^x \left( \frac{x - 1}{2 x^2} \right) dx\]
\[\int e^x \cdot \frac{\sqrt{1 - x^2} \sin^{- 1} x + 1}{\sqrt{1 - x^2}} \text{ dx }\]
\[\int\frac{2x + 1}{\left( x + 1 \right) \left( x - 2 \right)} dx\]
\[\int\frac{\cos x}{\left( 1 - \sin x \right)^3 \left( 2 + \sin x \right)} dx\]
\[\int\frac{x^2 - 1}{x^4 + 1} \text{ dx }\]
\[\int\frac{1}{1 - \cos x - \sin x} dx =\]
\[\int\frac{2}{\left( e^x + e^{- x} \right)^2} dx\]
\[\int\frac{\sin x}{\cos 2x} \text{ dx }\]
\[\int \cot^4 x\ dx\]
\[\int x\sqrt{2x + 3} \text{ dx }\]
\[\int\frac{\sin 2x}{\sin^4 x + \cos^4 x} \text{ dx }\]
\[\int\frac{1}{5 - 4 \sin x} \text{ dx }\]
\[\int\frac{6x + 5}{\sqrt{6 + x - 2 x^2}} \text{ dx}\]
\[\int\sqrt{a^2 + x^2} \text{ dx }\]
