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
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