Advertisements
Advertisements
प्रश्न
\[\int\frac{\sin 2x}{\left( a + b \cos 2x \right)^2} dx\]
योग
उत्तर
\[\int\frac{\sin \left( 2x \right)}{\left( a + b \cos 2x \right)^2}dx\]
\[\text{Let a + b }\cos2x = t\]
\[ \Rightarrow - \text{b }\sin \left( 2x \right) dx \times 2 = dt\]
\[ \Rightarrow \sin \left( 2x \right) dx = \frac{- dt}{2b}\]
\[Now, \int\frac{\sin \left( 2x \right)}{\left( a + b \cos 2x \right)^2}dx\]
\[ = - \frac{1}{2b}\int\frac{dt}{t^2}\]
\[ = \frac{- 1}{2b}\int t^{- 2} dt\]
\[ = \frac{- 1}{2b}\left[ \frac{t^{- 2 + 1}}{- 2 + 1} \right] + C\]
\[ = \frac{1}{2b} \times \frac{1}{t} + C\]
\[ = \frac{1}{2b \left( a + b \cos 2x \right)} + C\]
shaalaa.com
क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
APPEARS IN
संबंधित प्रश्न
\[\int\left( \frac{m}{x} + \frac{x}{m} + m^x + x^m + mx \right) dx\]
\[\int\frac{x^5 + x^{- 2} + 2}{x^2} dx\]
\[\int\frac{x}{\sqrt{x + a} - \sqrt{x + b}}dx\]
` ∫ sin 4x cos 7x dx `
\[\int\left\{ 1 + \tan x \tan \left( x + \theta \right) \right\} dx\]
\[\int\sqrt{1 + e^x} . e^x dx\]
\[\ ∫ x \text{ e}^{x^2} dx\]
\[\int\frac{x^2}{\sqrt{x - 1}} dx\]
\[\int\frac{x^2 + 3x + 1}{\left( x + 1 \right)^2} dx\]
\[\int\frac{1}{\sqrt{a^2 + b^2 x^2}} dx\]
\[\int\frac{1}{\sqrt{a^2 - b^2 x^2}} dx\]
\[\int\frac{x^4 + 1}{x^2 + 1} dx\]
\[\int\frac{\sec^2 x}{\sqrt{4 + \tan^2 x}} dx\]
\[\int\frac{x^3}{x^4 + x^2 + 1}dx\]
\[\int\frac{1}{3 + 2 \cos^2 x} \text{ dx }\]
\[\int\frac{1}{4 + 3 \tan x} dx\]
\[\int\cos\sqrt{x}\ dx\]
\[\int x\left( \frac{\sec 2x - 1}{\sec 2x + 1} \right) dx\]
∴\[\int e^{2x} \left( - \sin x + 2 \cos x \right) dx\]
\[\int\left( x + 2 \right) \sqrt{x^2 + x + 1} \text{ dx }\]
\[\int\frac{1}{\left( x - 1 \right) \left( x + 1 \right) \left( x + 2 \right)} dx\]
\[\int\frac{5 x^2 + 20x + 6}{x^3 + 2 x^2 + x} dx\]
\[\int\frac{x^2}{\left( x^2 + 1 \right) \left( 3 x^2 + 4 \right)} dx\]
Find \[\int\frac{2x}{\left( x^2 + 1 \right) \left( x^2 + 2 \right)^2}dx\]
\[\int\frac{x + 1}{\left( x - 1 \right) \sqrt{x + 2}} \text{ dx }\]
\[\int\frac{2}{\left( e^x + e^{- x} \right)^2} dx\]
\[\int\frac{\left( 2^x + 3^x \right)^2}{6^x} \text{ dx }\]
\[\int \text{cosec}^2 x \text{ cos}^2 \text{ 2x dx} \]
\[\int \tan^4 x\ dx\]
\[\int\frac{x^2}{\left( x - 1 \right)^3} dx\]
\[\int\frac{1}{x^2 + 4x - 5} \text{ dx }\]
\[\int\sqrt{\text{ cosec x} - 1} \text{ dx }\]
\[\int\frac{5x + 7}{\sqrt{\left( x - 5 \right) \left( x - 4 \right)}} \text{ dx }\]
\[\int\sqrt{\frac{1 - x}{x}} \text{ dx}\]
\[\int\frac{1}{\sec x + cosec x}\text{ dx }\]
\[\int\sqrt{x^2 - a^2} \text{ dx}\]
\[\int\sqrt{1 + 2x - 3 x^2}\text{ dx } \]
\[\int \left( x + 1 \right)^2 e^x \text{ dx }\]
\[\int \tan^{- 1} \sqrt{\frac{1 - x}{1 + x}} \text{ dx }\]
\[\int\frac{1}{1 + x + x^2 + x^3} \text{ dx }\]
