Advertisements
Advertisements
Question
\[\int\frac{e^{m \tan^{- 1} x}}{1 + x^2} dx\]
Sum
Advertisements
Solution
\[\int\left( \frac{e^{m \tan^{- 1} x}}{1 + x^2} \right)dx\]
\[\text{Let} \tan^{- 1} x = t\]
\[ \Rightarrow \left( \frac{1}{1 + x^2} \right)dx = dt\]
\[Now, \int\left( \frac{e^{m \tan^{- 1} x}}{1 + x^2} \right)dx\]
\[ = \int e^{mt} dt\]
\[ = \frac{e^{mt}}{m} + C\]
\[ = \frac{e^{m \tan^{- 1} x}}{m} + C\]
shaalaa.com
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
\[\int \left( 3x + 4 \right)^2 dx\]
If f' (x) = x − \[\frac{1}{x^2}\] and f (1) \[\frac{1}{2}, find f(x)\]
\[\int\frac{x^2 + 5x + 2}{x + 2} dx\]
\[\int\frac{2x + 1}{\sqrt{3x + 2}} dx\]
` ∫ cos mx cos nx dx `
\[\int\frac{\sin 2x}{a^2 + b^2 \sin^2 x} dx\]
` ∫ e^{m sin ^-1 x}/ \sqrt{1-x^2} ` dx
\[\int\frac{x + \sqrt{x + 1}}{x + 2} dx\]
\[\int \cot^5 \text{ x } {cosec}^4 x\text{ dx }\]
\[\int\frac{e^x}{e^{2x} + 5 e^x + 6} dx\]
\[\int\frac{1}{\sqrt{16 - 6x - x^2}} dx\]
\[\int\frac{1}{\sqrt{\left( 1 - x^2 \right)\left\{ 9 + \left( \sin^{- 1} x \right)^2 \right\}}} dx\]
\[\int\frac{x^3}{x^4 + x^2 + 1}dx\]
\[\int\frac{x^2 + x - 1}{x^2 + x - 6}\text{ dx }\]
\[\int\frac{6x - 5}{\sqrt{3 x^2 - 5x + 1}} \text{ dx }\]
\[\int\frac{2x + 5}{\sqrt{x^2 + 2x + 5}} dx\]
\[\int\sqrt{\frac{1 - x}{1 + x}} \text{ dx }\]
\[\int\frac{1}{5 + 7 \cos x + \sin x} dx\]
\[\int\frac{8 \cot x + 1}{3 \cot x + 2} \text{ dx }\]
\[\int x \cos x\ dx\]
` ∫ sin x log (\text{ cos x ) } dx `
\[\int e^\sqrt{x} \text{ dx }\]
\[\int\frac{x^2 \tan^{- 1} x}{1 + x^2} \text{ dx }\]
\[\int\left( e^\text{log x} + \sin x \right) \text{ cos x dx }\]
\[\int x \sin^3 x\ dx\]
\[\int\sqrt{x^2 - 2x} \text{ dx}\]
\[\int\frac{x^2 + 1}{\left( 2x + 1 \right) \left( x^2 - 1 \right)} dx\]
\[\int\frac{x^2}{\left( x - 1 \right) \left( x + 1 \right)^2} dx\]
\[\int\frac{x^3 - 1}{x^3 + x} dx\]
\[\int\frac{x^2 + 9}{x^4 + 81} \text{ dx }\]
\[\int \sin^4 2x\ dx\]
\[\int\frac{1}{1 + 2 \cos x} \text{ dx }\]
\[\int\frac{\sin^6 x}{\cos x} \text{ dx }\]
\[\int \tan^5 x\ \sec^3 x\ dx\]
\[\int\sqrt{3 x^2 + 4x + 1}\text{ dx }\]
\[\int \log_{10} x\ dx\]
\[\int x^2 \tan^{- 1} x\ dx\]
\[\int\frac{\cot x + \cot^3 x}{1 + \cot^3 x} \text{ dx}\]
\[\int \sin^3 \left( 2x + 1 \right) \text{dx}\]
