Mathematics

# Evaluate the following integral:$\int { { x }^{ 3 }\cos {x}^{ 4 } } dx$

##### SOLUTION
Let
$t={x}^{4}\Rightarrow\,dt=4{x}^{3}dx$

$\displaystyle\int{{x}^{3}\cos{{x}^{4}}dx}$

$=\dfrac{1}{4}\displaystyle\int{\cos{t}dt}$

$=\dfrac{1}{4}\sin{t}+c$

$=\dfrac{1}{4}\sin{{x}^{4}}+c$ where $t={x}^{4}$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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