Advertisements
Advertisements
Question
\[\int\frac{\sin \left( \tan^{- 1} x \right)}{1 + x^2} dx\]
Sum
Advertisements
Solution
\[\int\frac{\sin \left( \tan^{- 1} x \right)}{1 + x^2}dx\]
\[\text{Let} \tan^{- 1} x = t\]
\[ \Rightarrow \frac{1}{1 + x^2}dx = dt\]
\[Now, \int\frac{\sin \left( \tan^{- 1} x \right)}{1 + x^2}dx\]
\[ = \int\text{sin t dt} \]
\[ = - \cos \left( t \right) + C\]
\[ = - \cos \left( \tan^{- 1} x \right) + C\]
shaalaa.com
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
\[\int\frac{\left( 1 + x \right)^3}{\sqrt{x}} dx\]
\[\int\frac{x^5 + x^{- 2} + 2}{x^2} dx\]
\[\int\frac{\sin^3 x - \cos^3 x}{\sin^2 x \cos^2 x} dx\]
\[\int \cos^2 \frac{x}{2} dx\]
\[\int \cos^2 \text{nx dx}\]
` ∫ cos 3x cos 4x` dx
\[\int\frac{1}{\sqrt{1 + \cos x}} dx\]
` ∫ {"cosec" x }/ { log tan x/2 ` dx
\[\int x^2 e^{x^3} \cos \left( e^{x^3} \right) dx\]
\[\int x^2 \sqrt{x + 2} \text{ dx }\]
\[\ \int\ x \left( 1 - x \right)^{23} dx\]
\[\int \sin^5 x \cos x \text{ dx }\]
Evaluate the following integrals:
\[\int\cos\left\{ 2 \cot^{- 1} \sqrt{\frac{1 + x}{1 - x}} \right\}dx\]
\[\int\frac{1}{x \left( x^6 + 1 \right)} dx\]
\[\int\frac{x}{x^4 - x^2 + 1} dx\]
\[\int\frac{x}{3 x^4 - 18 x^2 + 11} dx\]
\[\int\frac{1}{\sqrt{7 - 3x - 2 x^2}} dx\]
\[\int\frac{x^2}{x^2 + 7x + 10} dx\]
\[\int\frac{1}{4 \cos^2 x + 9 \sin^2 x}\text{ dx }\]
\[\int\frac{1}{1 - 2 \sin x} \text{ dx }\]
\[\int\frac{1}{1 - \cot x} dx\]
\[\int x^2 e^{- x} \text{ dx }\]
\[\int \left( \log x \right)^2 \cdot x\ dx\]
\[\int \sin^{- 1} \left( \frac{2x}{1 + x^2} \right) \text{ dx }\]
\[\int\left( 2x - 5 \right) \sqrt{x^2 - 4x + 3} \text{ dx }\]
\[\int\frac{x^2 + 1}{x^2 - 1} dx\]
\[\int\frac{5x}{\left( x + 1 \right) \left( x^2 - 4 \right)} dx\]
\[\int\frac{x^2}{\left( x - 1 \right) \left( x + 1 \right)^2} dx\]
\[\int\frac{1}{\sin x + \sin 2x} dx\]
\[\int\frac{x^2 + 1}{x^4 + x^2 + 1} \text{ dx }\]
\[\int\frac{1}{\left( x + 1 \right) \sqrt{x^2 + x + 1}} \text{ dx }\]
\[\int \sec^2 x \cos^2 2x \text{ dx }\]
\[\int\sin x \sin 2x \text{ sin 3x dx }\]
\[\int\frac{1}{\text{ sin} \left( x - a \right) \text{ sin } \left( x - b \right)} \text{ dx }\]
\[\int\frac{\sin x}{\cos 2x} \text{ dx }\]
\[\int\frac{1}{\left( \sin x - 2 \cos x \right) \left( 2 \sin x + \cos x \right)} \text{ dx }\]
\[\int\frac{\cos x}{\frac{1}{4} - \cos^2 x} \text{ dx }\]
\[\int\frac{6x + 5}{\sqrt{6 + x - 2 x^2}} \text{ dx}\]
\[\int\frac{\cos^7 x}{\sin x} dx\]
