Advertisements
Advertisements
प्रश्न
\[\int \left( a \tan x + b \cot x \right)^2 dx\]
योग
उत्तर
\[\int \left( a \tan x + b \cot x \right)^2 dx\]
\[ = \int\left( a^2 \tan^2 x + b^2 \cot^2 x +\text{ 2ab tan x }\cot x \right)dx\]
\[ = a^2 \int \tan^2\text{ x dx }+ b^2 \int \cot^2 \text{x dx }+ \text{2ab ∫ dx}\]
\[ = a^2 \int\left( \sec^2 x - 1 \right)dx + b^2 \int\left( {cosec}^2 x - 1 \right)dx + 2ab\ ∫ dx\]
\[ = a^2 \left[ \tan x - x \right] + b^2 \left[ - \cot x - x \right] + \text{2ab x }+ C\]
\[ = a^2 \tan x - b^2 \cot x - \left( a^2 + b^2 - 2ab \right)x + C\]
shaalaa.com
क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
APPEARS IN
संबंधित प्रश्न
\[\int\frac{x^5 + x^{- 2} + 2}{x^2} dx\]
\[\int\left( \sec^2 x + {cosec}^2 x \right) dx\]
\[\int\frac{\sin^3 x - \cos^3 x}{\sin^2 x \cos^2 x} dx\]
\[\int\frac{1}{\sqrt{1 + \cos x}} dx\]
\[\int\frac{\text{sin} \left( x - a \right)}{\text{sin}\left( x - b \right)} dx\]
\[\int\frac{\sec x \tan x}{3 \sec x + 5} dx\]
\[\int\left( 4x + 2 \right)\sqrt{x^2 + x + 1} \text{dx}\]
\[\int\frac{1}{1 + \sqrt{x}} dx\]
` ∫ e^{m sin ^-1 x}/ \sqrt{1-x^2} ` dx
\[\int\frac{1}{x^2 \left( x^4 + 1 \right)^{3/4}} dx\]
\[\int\frac{x^2}{\sqrt{3x + 4}} dx\]
` ∫ tan^3 x sec^2 x dx `
\[\int\frac{x^2}{x^2 + 6x + 12} \text{ dx }\]
\[\int\frac{x + 1}{\sqrt{x^2 + 1}} dx\]
\[\int\sqrt{\frac{1 - x}{1 + x}} \text{ dx }\]
\[\int x e^{2x} \text{ dx }\]
\[\int x^2 e^{- x} \text{ dx }\]
\[\int \sin^{- 1} \sqrt{x} \text{ dx }\]
\[\int \sin^{- 1} \left( 3x - 4 x^3 \right) \text{ dx }\]
\[\int x \sin^3 x\ dx\]
\[\int\frac{x^2 \sin^{- 1} x}{\left( 1 - x^2 \right)^{3/2}} \text{ dx }\]
\[\int e^x \left( \frac{\sin x \cos x - 1}{\sin^2 x} \right) dx\]
\[\int\frac{2x - 3}{\left( x^2 - 1 \right) \left( 2x + 3 \right)} dx\]
\[\int\frac{\sin 2x}{\left( 1 + \sin x \right) \left( 2 + \sin x \right)} dx\]
\[\int\frac{5}{\left( x^2 + 1 \right) \left( x + 2 \right)} dx\]
\[\int\frac{x}{\left( x + 1 \right) \left( x^2 + 1 \right)} dx\]
\[\int\frac{2x + 1}{\left( x - 2 \right) \left( x - 3 \right)} dx\]
\[\int\frac{x^2 + 1}{x^4 + x^2 + 1} \text{ dx }\]
\[\int\frac{\left( x - 1 \right)^2}{x^4 + x^2 + 1} \text{ dx}\]
\[\int\frac{1}{\left( 2 x^2 + 3 \right) \sqrt{x^2 - 4}} \text{ dx }\]
\[\int\left( x - 1 \right) e^{- x} dx\] is equal to
The value of \[\int\frac{\sin x + \cos x}{\sqrt{1 - \sin 2x}} dx\] is equal to
\[\int \text{cosec}^2 x \text{ cos}^2 \text{ 2x dx} \]
\[\int \sin^3 x \cos^4 x\ \text{ dx }\]
\[\int\frac{1}{\sqrt{x^2 + a^2}} \text{ dx }\]
\[\int\sqrt{\frac{1 - x}{x}} \text{ dx}\]
\[\int\frac{1}{1 - 2 \sin x} \text{ dx }\]
\[\int\frac{1}{1 + x + x^2 + x^3} \text{ dx }\]
