Advertisements
Advertisements
Question
\[\int x^2 e^{x^3} \cos \left( e^{x^3} \right) dx\]
Sum
Advertisements
Solution
\[\int x^2 \cdot e^{x^3} \cdot \cos \left( e^{x^3} \right) dx\]
\[\text{Let e}^{x^3} = t\]
\[ \Rightarrow e^{x^3} \cdot 3 x^2 dx = dt\]
\[ \Rightarrow e^{x^3} \cdot x^2 dx = \frac{dt}{3}\]
\[Now, \int x^2 \cdot e^{x^3} \cdot \cos \left( e^{x^3} \right) dx\]
\[ = \frac{1}{3}\int\cos\left( t \right) dt\]
\[ = \frac{1}{3}\left[ \sin t \right] + C\]
\[ = \frac{1}{3}\left[ \sin \left( e^{x^3} \right) \right] + C\]
shaalaa.com
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
\[\int\left( x^e + e^x + e^e \right) dx\]
\[\int\frac{\cos x}{1 - \cos x} \text{dx }or \int\frac{\cot x}{\text{cosec } {x }- \cot x} dx\]
\[\int\frac{1}{\sqrt{2x + 3} + \sqrt{2x - 3}} dx\]
` ∫ cos 3x cos 4x` dx
\[\int\frac{1 - \cot x}{1 + \cot x} dx\]
\[\int\frac{\cos x}{2 + 3 \sin x} dx\]
\[\int\frac{\sin 2x}{a^2 + b^2 \sin^2 x} dx\]
\[\int\frac{1}{1 + \sqrt{x}} dx\]
\[\int\frac{\sin^5 x}{\cos^4 x} \text{ dx }\]
\[\int\left( 2 x^2 + 3 \right) \sqrt{x + 2} \text{ dx }\]
` ∫ tan^5 x dx `
\[\int \cot^5 \text{ x } {cosec}^4 x\text{ dx }\]
\[\int \cot^5 x \text{ dx }\]
\[\int\frac{e^x}{\sqrt{16 - e^{2x}}} dx\]
\[\int\frac{1}{\sqrt{\left( 1 - x^2 \right)\left\{ 9 + \left( \sin^{- 1} x \right)^2 \right\}}} dx\]
\[\int\frac{\sin x - \cos x}{\sqrt{\sin 2x}} dx\]
\[\int\frac{2x - 3}{x^2 + 6x + 13} dx\]
\[\int\frac{x^2 + x - 1}{x^2 + x - 6}\text{ dx }\]
\[\int\frac{1}{3 + 2 \cos^2 x} \text{ dx }\]
`int"x"^"n"."log" "x" "dx"`
\[\int x^2 \sin^{- 1} x\ dx\]
\[\int \tan^{- 1} \left( \frac{2x}{1 - x^2} \right) \text{ dx }\]
\[\int \sin^3 \sqrt{x}\ dx\]
\[\int\frac{x}{\left( x^2 - a^2 \right) \left( x^2 - b^2 \right)} dx\]
\[\int\frac{x^2}{\left( x - 1 \right) \left( x + 1 \right)^2} dx\]
\[\int\frac{x^2 + x - 1}{\left( x + 1 \right)^2 \left( x + 2 \right)} dx\]
\[\int\frac{x^2}{\left( x - 1 \right) \sqrt{x + 2}}\text{ dx}\]
\[\int\left( x - 1 \right) e^{- x} dx\] is equal to
If `int(2x^(1/2))/(x^2) dx = k . 2^(1/x) + C`, then k is equal to ______.
\[\int\frac{1}{\text{ cos }\left( x - a \right) \text{ cos }\left( x - b \right)} \text{ dx }\]
\[\int \tan^5 x\ dx\]
\[\int \cot^4 x\ dx\]
\[\int\frac{1}{\sqrt{3 - 2x - x^2}} \text{ dx}\]
\[\int\frac{x + 1}{x^2 + 4x + 5} \text{ dx}\]
\[\int\sqrt{\frac{1 - x}{x}} \text{ dx}\]
\[\int\frac{1}{\sec x + cosec x}\text{ dx }\]
\[\int \left( x + 1 \right)^2 e^x \text{ dx }\]
\[\int\frac{\log \left( 1 - x \right)}{x^2} \text{ dx}\]
\[\int \sin^{- 1} \sqrt{\frac{x}{a + x}} \text{ dx}\]
\[\int\frac{3x + 1}{\sqrt{5 - 2x - x^2}} \text{ dx }\]
