Advertisements
Advertisements
प्रश्न
\[\int\frac{\sin \left( \tan^{- 1} x \right)}{1 + x^2} dx\]
योग
Advertisements
उत्तर
\[\int\frac{\sin \left( \tan^{- 1} x \right)}{1 + x^2}dx\]
\[\text{Let} \tan^{- 1} x = t\]
\[ \Rightarrow \frac{1}{1 + x^2}dx = dt\]
\[Now, \int\frac{\sin \left( \tan^{- 1} x \right)}{1 + x^2}dx\]
\[ = \int\text{sin t dt} \]
\[ = - \cos \left( t \right) + C\]
\[ = - \cos \left( \tan^{- 1} x \right) + C\]
shaalaa.com
क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
APPEARS IN
संबंधित प्रश्न
`int{sqrtx(ax^2+bx+c)}dx`
\[\int \left( \sqrt{x} - \frac{1}{\sqrt{x}} \right)^2 dx\]
\[\int\left( x^e + e^x + e^e \right) dx\]
If f' (x) = 8x3 − 2x, f(2) = 8, find f(x)
\[\int\frac{1 - \cos x}{1 + \cos x} dx\]
`∫ cos ^4 2x dx `
` ∫ sin 4x cos 7x dx `
\[\int\frac{x \sin^{- 1} x^2}{\sqrt{1 - x^4}} dx\]
\[\int\frac{\text{sin }\left( \text{2 + 3 log x }\right)}{x} dx\]
\[\int \cot^5 x \text{ dx }\]
\[\int \cos^5 x \text{ dx }\]
\[\int\frac{1}{1 + x - x^2} \text{ dx }\]
\[\int\frac{\sec^2 x}{1 - \tan^2 x} dx\]
\[\int\frac{\cos 2x}{\sqrt{\sin^2 2x + 8}} dx\]
\[\int\frac{1}{\sqrt{\left( 1 - x^2 \right)\left\{ 9 + \left( \sin^{- 1} x \right)^2 \right\}}} dx\]
\[\int\frac{x^2 + x + 1}{x^2 - x} dx\]
\[\int\frac{x^3 + x^2 + 2x + 1}{x^2 - x + 1}\text{ dx }\]
\[\int\frac{x^2}{x^2 + 6x + 12} \text{ dx }\]
\[\int\frac{2x + 1}{\sqrt{x^2 + 2x - 1}}\text{ dx }\]
\[\int\frac{2}{2 + \sin 2x}\text{ dx }\]
\[\int x \cos x\ dx\]
\[\int \sec^{- 1} \sqrt{x}\ dx\]
\[\int x^2 \tan^{- 1} x\text{ dx }\]
\[\int e^x \left( \cot x + \log \sin x \right) dx\]
\[\int\frac{1}{x\left( x - 2 \right) \left( x - 4 \right)} dx\]
\[\int\frac{x^2}{\left( x - 1 \right) \left( x - 2 \right) \left( x - 3 \right)} dx\]
\[\int\frac{\sin 2x}{\left( 1 + \sin x \right) \left( 2 + \sin x \right)} dx\]
\[\int\frac{3}{\left( 1 - x \right) \left( 1 + x^2 \right)} dx\]
\[\int\frac{1}{x^4 + x^2 + 1} \text{ dx }\]
\[\int\frac{x^2}{\left( x - 1 \right) \sqrt{x + 2}}\text{ dx}\]
\[\int\frac{1}{\left( x^2 + 1 \right) \sqrt{x}} \text{ dx }\]
If `int(2x^(1/2))/(x^2) dx = k . 2^(1/x) + C`, then k is equal to ______.
\[\int\frac{\sin x}{1 + \sin x} \text{ dx }\]
\[\int \cot^4 x\ dx\]
\[\int \cot^5 x\ dx\]
\[\int\frac{1}{1 - 2 \sin x} \text{ dx }\]
\[\int\sqrt{a^2 + x^2} \text{ dx }\]
\[\int\frac{x^2}{\sqrt{1 - x}} \text{ dx }\]
\[\int \left( e^x + 1 \right)^2 e^x dx\]
