Advertisements
Advertisements
Question
\[\ ∫ x \text{ e}^{x^2} dx\]
Sum
Advertisements
Solution
\[\int x . e^{x^2} dx\]
\[\text{Let x}^2 = t\]
\[ \Rightarrow \text{2x dx} = dt\]
\[ \Rightarrow \text{x dx} = \frac{dt}{2}\]
\[Now, \int x . e^{x^2} dx\]
\[ = \frac{1}{2}\int e^t dt\]
\[ = \frac{1}{2} e^t + C\]
\[ = \frac{1}{2} e^{x^2} + C\]
shaalaa.com
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
\[\int\frac{\left( 1 + \sqrt{x} \right)^2}{\sqrt{x}} dx\]
\[\int\frac{1 + \cos x}{1 - \cos x} dx\]
\[\int\sqrt{\frac{1 - \sin 2x}{1 + \sin 2x}} dx\]
` ∫ {sin 2x} /{a cos^2 x + b sin^2 x } ` dx
` ∫ tan 2x tan 3x tan 5x dx `
\[\int\sqrt{1 + e^x} . e^x dx\]
\[\int\frac{x}{\sqrt{x^2 + a^2} + \sqrt{x^2 - a^2}} dx\]
\[\int 5^{5^{5^x}} 5^{5^x} 5^x dx\]
\[\int\frac{1}{\left( x + 1 \right)\left( x^2 + 2x + 2 \right)} dx\]
\[\int \cot^6 x \text{ dx }\]
` ∫ {1}/{a^2 x^2- b^2}dx`
\[\int\frac{1}{\sqrt{\left( 2 - x \right)^2 + 1}} dx\]
\[\int\frac{x^4 + 1}{x^2 + 1} dx\]
\[\int\frac{x + 2}{2 x^2 + 6x + 5}\text{ dx }\]
\[\int\frac{x^2 + 1}{x^2 - 5x + 6} dx\]
\[\int\frac{5x + 3}{\sqrt{x^2 + 4x + 10}} \text{ dx }\]
`int 1/(sin x - sqrt3 cos x) dx`
\[\int\frac{3 + 2 \cos x + 4 \sin x}{2 \sin x + \cos x + 3} \text{ dx }\]
\[\int x \cos x\ dx\]
\[\int\cos\sqrt{x}\ dx\]
\[\int e^x \left[ \sec x + \log \left( \sec x + \tan x \right) \right] dx\]
\[\int e^x \left( \log x + \frac{1}{x^2} \right) dx\]
\[\int\sqrt{2ax - x^2} \text{ dx}\]
\[\int\sqrt{x^2 - 2x} \text{ dx}\]
\[\int\left( x + 1 \right) \sqrt{x^2 - x + 1} \text{ dx}\]
\[\int\left( 4x + 1 \right) \sqrt{x^2 - x - 2} \text{ dx }\]
\[\int\left( 2x + 3 \right) \sqrt{x^2 + 4x + 3} \text{ dx }\]
\[\int\left( 2x - 5 \right) \sqrt{x^2 - 4x + 3} \text{ dx }\]
\[\int\frac{x^2}{\left( x - 1 \right) \sqrt{x + 2}}\text{ dx}\]
\[\int\frac{x}{\left( x^2 + 4 \right) \sqrt{x^2 + 9}} \text{ dx}\]
Write a value of
\[\int e^{3 \text{ log x}} x^4\text{ dx}\]
If \[\int\frac{\cos 8x + 1}{\tan 2x - \cot 2x} dx\]
\[\int\frac{1}{7 + 5 \cos x} dx =\]
\[\int \cos^3 (3x)\ dx\]
\[\int \cot^4 x\ dx\]
\[\int \cos^5 x\ dx\]
\[\int\frac{5x + 7}{\sqrt{\left( x - 5 \right) \left( x - 4 \right)}} \text{ dx }\]
\[\int \sec^4 x\ dx\]
\[\int\frac{1}{2 + \cos x} \text{ dx }\]
\[\int\frac{1}{x \sqrt{1 + x^n}} \text{ dx}\]
