Advertisements
Advertisements
Question
\[\int\left( x^e + e^x + e^e \right) dx\]
Sum
Advertisements
Solution
\[\int\left( x^e + e^x + e^e \right)dx\]
\[ = \int x^e dx + \int e^x dx + e^e \int1dx\]
\[ = \frac{x^{e + 1}}{e + 1} + e^x + x \cdot e^e + C\]
shaalaa.com
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
\[\int\left( 3x\sqrt{x} + 4\sqrt{x} + 5 \right)dx\]
\[\int\sqrt{x}\left( x^3 - \frac{2}{x} \right) dx\]
\[\int\frac{\sin^2 x}{1 + \cos x} \text{dx} \]
\[\int\frac{1 - \cos 2x}{1 + \cos 2x} dx\]
\[\int\frac{1}{1 + \cos 2x} dx\]
\[\int\frac{1 - \cos x}{1 + \cos x} dx\]
\[\int\frac{x}{\sqrt{x + a} - \sqrt{x + b}}dx\]
\[\int\frac{\cos 4x - \cos 2x}{\sin 4x - \sin 2x} dx\]
\[\int\frac{\sec^2 x}{\tan x + 2} dx\]
\[\int\frac{1}{1 + \sqrt{x}} dx\]
\[\int\frac{x + \sqrt{x + 1}}{x + 2} dx\]
\[\int\frac{x^2}{\sqrt{1 - x}} dx\]
` = ∫1/{sin^3 x cos^ 2x} dx`
Evaluate the following integrals:
\[\int\cos\left\{ 2 \cot^{- 1} \sqrt{\frac{1 + x}{1 - x}} \right\}dx\]
\[\int\frac{x^2}{x^6 + a^6} dx\]
\[\int\frac{x^2 + x + 1}{x^2 - x} dx\]
\[\int\frac{x^2 + x - 1}{x^2 + x - 6}\text{ dx }\]
\[\int\frac{1}{\left( \sin x - 2 \cos x \right)\left( 2 \sin x + \cos x \right)} \text{ dx }\]
\[\int\frac{\log \left( \log x \right)}{x} dx\]
\[\int\frac{x + \sin x}{1 + \cos x} \text{ dx }\]
` ∫ x tan ^2 x dx
\[\int x \sin^3 x\ dx\]
\[\int e^x \frac{1 + x}{\left( 2 + x \right)^2} \text{ dx }\]
\[\int x\sqrt{x^4 + 1} \text{ dx}\]
\[\int\left( 4x + 1 \right) \sqrt{x^2 - x - 2} \text{ dx }\]
\[\int\frac{x^2 + x - 1}{x^2 + x - 6} dx\]
\[\int\frac{x^2 + 1}{\left( 2x + 1 \right) \left( x^2 - 1 \right)} dx\]
\[\int\frac{x}{\left( x^2 - a^2 \right) \left( x^2 - b^2 \right)} dx\]
\[\int\sqrt{\cot \text{θ} d } \text{ θ}\]
\[\int\frac{1}{\left( x - 1 \right) \sqrt{x + 2}} \text{ dx }\]
\[\int x \sin^5 x^2 \cos x^2 dx\]
\[\int\frac{\sin x}{\sqrt{\cos^2 x - 2 \cos x - 3}} \text{ dx }\]
\[\int\frac{\sqrt{a} - \sqrt{x}}{1 - \sqrt{ax}}\text{ dx }\]
\[\int\frac{1}{2 - 3 \cos 2x} \text{ dx }\]
\[\int\frac{1}{1 - 2 \sin x} \text{ dx }\]
\[\int\frac{1}{2 + \cos x} \text{ dx }\]
\[\int\sqrt{\frac{a + x}{x}}dx\]
\[\int \tan^3 x\ \sec^4 x\ dx\]
\[\int \left( x + 1 \right)^2 e^x \text{ dx }\]
