Advertisements
Advertisements
Question
\[\int x^3 \cos x^4 dx\]
Sum
Advertisements
Solution
\[\int x^3 \cdot \cos \left( x^4 \right) dx\]
\[\text{Let x}^4 = t\]
\[ \Rightarrow 4 x^3 dx = dt\]
\[ \Rightarrow x^3 dx = \frac{dt}{4}\]
\[Now, \int x^3 \cdot \cos \left( x^4 \right) dx\]
\[ = \frac{1}{4}\int\cos \left( t \right) dt\]
\[ = \frac{1}{4}\left[ \text{sin} \left( t \right) \right] + C\]
\[ = \frac{1}{4}\left[ \text{sin x}^4 \right] + C\]
shaalaa.com
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
`int{sqrtx(ax^2+bx+c)}dx`
\[\int\sqrt{x}\left( x^3 - \frac{2}{x} \right) dx\]
\[\int\frac{\left( x + 1 \right)\left( x - 2 \right)}{\sqrt{x}} dx\]
\[\int\frac{\sin^2 x}{1 + \cos x} \text{dx} \]
\[\int\frac{\sin^3 x - \cos^3 x}{\sin^2 x \cos^2 x} dx\]
\[\int\frac{1}{\sqrt{2x + 3} + \sqrt{2x - 3}} dx\]
\[\int\frac{x^2 + 3x - 1}{\left( x + 1 \right)^2} dx\]
\[\int \text{sin}^2 \left( 2x + 5 \right) \text{dx}\]
\[\int\frac{x + 1}{x \left( x + \log x \right)} dx\]
\[\int\frac{\sin \left( \tan^{- 1} x \right)}{1 + x^2} dx\]
\[\ ∫ x \text{ e}^{x^2} dx\]
\[\int 5^{5^{5^x}} 5^{5^x} 5^x dx\]
\[\int\frac{1}{\left( x + 1 \right)\left( x^2 + 2x + 2 \right)} dx\]
\[\int\left( 2 x^2 + 3 \right) \sqrt{x + 2} \text{ dx }\]
` ∫ tan^5 x sec ^4 x dx `
\[\int \cos^7 x \text{ dx } \]
\[\int\frac{1}{x^2 - 10x + 34} dx\]
\[\int\frac{\cos x}{\sin^2 x + 4 \sin x + 5} dx\]
\[\int\frac{e^x}{\left( 1 + e^x \right)\left( 2 + e^x \right)} dx\]
\[\int\frac{1}{\sqrt{7 - 6x - x^2}} dx\]
\[\int\frac{2x + 5}{x^2 - x - 2} \text{ dx }\]
\[\int\frac{\left( 3 \sin x - 2 \right) \cos x}{5 - \cos^2 x - 4 \sin x} dx\]
\[\int\frac{\left( 3\sin x - 2 \right)\cos x}{13 - \cos^2 x - 7\sin x}dx\]
\[\int\frac{x + 7}{3 x^2 + 25x + 28}\text{ dx}\]
\[\int\frac{1}{3 + 2 \cos^2 x} \text{ dx }\]
\[\int x^2 \text{ cos x dx }\]
` ∫ sin x log (\text{ cos x ) } dx `
\[\int \log_{10} x\ dx\]
\[\int\frac{x^3 \sin^{- 1} x^2}{\sqrt{1 - x^4}} \text{ dx }\]
\[\int e^x \left( \log x + \frac{1}{x} \right) dx\]
\[\int\frac{18}{\left( x + 2 \right) \left( x^2 + 4 \right)} dx\]
\[\int\frac{5}{\left( x^2 + 1 \right) \left( x + 2 \right)} dx\]
\[\int\frac{1}{\left( x^2 + 1 \right) \left( x^2 + 2 \right)} dx\]
Evaluate the following integral:
\[\int\frac{x^2}{1 - x^4}dx\]
\[\int\frac{\sin x}{3 + 4 \cos^2 x} dx\]
\[\int\frac{\sin^2 x}{\cos^4 x} dx =\]
\[\int\frac{1}{\left( \sin^{- 1} x \right) \sqrt{1 - x^2}} \text{ dx} \]
\[\int\frac{1}{e^x + 1} \text{ dx }\]
\[\int\sqrt{1 + 2x - 3 x^2}\text{ dx } \]
