Advertisements
Advertisements
प्रश्न
\[\int\frac{1 - \cos x}{1 + \cos x} dx\]
योग
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
क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
APPEARS IN
संबंधित प्रश्न
\[\int\frac{\left( 1 + x \right)^3}{\sqrt{x}} dx\]
\[\int\frac{x^3 - 3 x^2 + 5x - 7 + x^2 a^x}{2 x^2} dx\]
If f' (x) = x − \[\frac{1}{x^2}\] and f (1) \[\frac{1}{2}, find f(x)\]
\[\int \cos^2 \frac{x}{2} dx\]
\[\int\frac{2 \cos 2x + \sec^2 x}{\sin 2x + \tan x - 5} dx\]
\[\int\frac{\log\left( 1 + \frac{1}{x} \right)}{x \left( 1 + x \right)} dx\]
\[\int\left( 4x + 2 \right)\sqrt{x^2 + x + 1} \text{dx}\]
\[\int x^3 \cos x^4 dx\]
\[\int\frac{\cos^5 x}{\sin x} dx\]
\[\int\frac{x^2}{\sqrt{x - 1}} dx\]
` ∫ 1 /{x^{1/3} ( x^{1/3} -1)} ` dx
\[\int \cot^6 x \text{ dx }\]
\[\int \sin^3 x \cos^6 x \text{ dx }\]
Evaluate the following integrals:
\[\int\frac{x^2}{\left( a^2 - x^2 \right)^{3/2}}dx\]
\[\int\frac{x + 2}{\sqrt{x^2 - 1}} \text{ dx }\]
\[\int\frac{1}{1 - \sin x + \cos x} \text{ dx }\]
\[\int\frac{1}{3 + 4 \cot x} dx\]
\[\int\text{ log }\left( x + 1 \right) \text{ dx }\]
`int"x"^"n"."log" "x" "dx"`
\[\int {cosec}^3 x\ dx\]
\[\int\frac{x^2 \tan^{- 1} x}{1 + x^2} \text{ dx }\]
\[\int\left( x + 1 \right) \text{ log x dx }\]
\[\int \sin^{- 1} \sqrt{\frac{x}{a + x}} \text{ dx }\]
\[\int e^x \left( \frac{1}{x^2} - \frac{2}{x^3} \right) dx\]
\[\int e^x \left( \log x + \frac{1}{x} \right) dx\]
\[\int\sqrt{3 - x^2} \text{ dx}\]
\[\int\left( x + 1 \right) \sqrt{x^2 + x + 1} \text{ dx }\]
\[\int\frac{x^2 + 1}{x\left( x^2 - 1 \right)} dx\]
\[\int\frac{1}{x\left( x^n + 1 \right)} dx\]
\[\int\frac{1}{\left( x + 1 \right)^2 \left( x^2 + 1 \right)} dx\]
\[\int\frac{1}{\cos x \left( 5 - 4 \sin x \right)} dx\]
\[\int\frac{1}{\sin x + \sin 2x} dx\]
\[\int\frac{x}{\left( x^2 + 4 \right) \sqrt{x^2 + 1}} \text{ dx }\]
\[\int\frac{1}{5 - 4 \sin x} \text{ dx }\]
\[\int\frac{\sin^2 x}{\cos^6 x} \text{ dx }\]
\[\int x\sqrt{\frac{1 - x}{1 + x}} \text{ dx }\]
\[\int \sin^{- 1} \sqrt{\frac{x}{a + x}} \text{ dx}\]
\[\int \cos^{- 1} \left( 1 - 2 x^2 \right) \text{ dx }\]
