Advertisements
Advertisements
प्रश्न
\[\int\frac{1 + \cos 4x}{\cot x - \tan x} dx\]
योग
उत्तर
\[\int\left( \frac{1 + \cos 4x}{\cot x - \tan x} \right) dx\]
\[ = \int\frac{\left( 1 + \cos 4x \right)}{\left( \frac{\cos x}{\sin x} - \frac{\sin x}{\cos x} \right)} dx\]
\[ = \int\frac{2 \cos^2 2x \times \sin x \cos x}{\left( \cos^2 x - \sin^2 x \right)}dx\]
\[ = \int\frac{\cos^2 2x \times 2 \sin x \cos x}{\cos 2x}dx\]
\[ = \int\cos 2x \sin 2xdx\]
\[ = \frac{1}{2}\int2 \sin 2x \cos 2xdx\]
\[ = \frac{1}{2}\int\sin 4xdx\]
\[ = \frac{1}{2}\left[ - \frac{\cos 4x}{4} \right] + C\]
\[ = - \frac{1}{8}\cos 4x + C\]
shaalaa.com
क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
APPEARS IN
संबंधित प्रश्न
\[\int \left( \sqrt{x} - \frac{1}{\sqrt{x}} \right)^2 dx\]
\[\int \left( 2x - 3 \right)^5 + \sqrt{3x + 2} \text{dx} \]
` ∫ cos 3x cos 4x` dx
\[\int\sqrt{\frac{1 + \cos 2x}{1 - \cos 2x}} dx\]
\[\int\frac{e^{3x}}{e^{3x} + 1} dx\]
\[\int\frac{2 \cos 2x + \sec^2 x}{\sin 2x + \tan x - 5} dx\]
\[\int\frac{\left( 1 + \sqrt{x} \right)^2}{\sqrt{x}} dx\]
\[\int\frac{1}{\sqrt{x} + x} \text{ dx }\]
\[\int \cot^5 x \text{ dx }\]
\[\int\frac{1}{\sin x \cos^3 x} dx\]
\[\int\frac{\sin 2x}{\sqrt{\cos^4 x - \sin^2 x + 2}} dx\]
\[\int\frac{3x + 1}{\sqrt{5 - 2x - x^2}} \text{ dx }\]
\[\int x^2 e^{- x} \text{ dx }\]
\[\int\cos\sqrt{x}\ dx\]
\[\int e^x \left( \frac{x - 1}{2 x^2} \right) dx\]
\[\int e^x \left( \frac{x - 1}{2 x^2} \right) dx\]
\[\int e^x \sec x \left( 1 + \tan x \right) dx\]
\[\int e^x \frac{1 + x}{\left( 2 + x \right)^2} \text{ dx }\]
\[\int x\sqrt{x^4 + 1} \text{ dx}\]
\[\int\frac{x^2 + 1}{x\left( x^2 - 1 \right)} dx\]
\[\int\frac{x}{\left( x - 1 \right)^2 \left( x + 2 \right)} dx\]
\[\int\frac{18}{\left( x + 2 \right) \left( x^2 + 4 \right)} dx\]
\[\int\frac{\cos x}{\left( 1 - \sin x \right)^3 \left( 2 + \sin x \right)} dx\]
\[\int\frac{1}{\left( x^2 + 1 \right) \left( x^2 + 2 \right)} dx\]
\[\int\sqrt{\cot \text{θ} d } \text{ θ}\]
\[\int\frac{\cos2x - \cos2\theta}{\cos x - \cos\theta}dx\] is equal to
\[\int\frac{x + 2}{\left( x + 1 \right)^3} \text{ dx }\]
\[\int\frac{\sin x - \cos x}{\sqrt{\sin 2x}} \text{ dx }\]
\[\int\frac{\sin 2x}{\sin^4 x + \cos^4 x} \text{ dx }\]
\[\int\frac{\sin x}{\sqrt{\cos^2 x - 2 \cos x - 3}} \text{ dx }\]
\[\int\frac{5x + 7}{\sqrt{\left( x - 5 \right) \left( x - 4 \right)}} \text{ dx }\]
\[\int\sqrt{\frac{1 + x}{x}} \text{ dx }\]
\[\int\frac{\sin^2 x}{\cos^6 x} \text{ dx }\]
\[\int \tan^5 x\ \sec^3 x\ dx\]
\[\int\frac{\log \left( 1 - x \right)}{x^2} \text{ dx}\]
\[\int x^3 \left( \log x \right)^2\text{ dx }\]
\[\int\frac{x}{x^3 - 1} \text{ dx}\]
