Question

int x^(4)sin(x^(5)+6)dx` is equal to: `​

Answer 1

this is an answer.....

Answer 2

$\boxed{\int x^4\sin(x^5+6)dx=-\frac{1}{5}\cos(x^5+6)+C}$

Step-by-step explanation:

Given:

$x^4\sin(x^5+6)$

To find out:

Integration of $x^4\sin(x^5+6)$

Solution

$\int x^4\sin(x^5+6)dx=?$

Let $x^5+6=t$

$\frac{dt}{dx}=5x^4$

$\implies dt=5x^4dx$

Now

$\int x^4\sin(x^5+6)dx$

$=\int \frac{1}{5}\sin tdt$

$=\frac{1}{5}\int \sin tdt$

$=\frac{1}{5}(-\cos t)+C$ where C is an arbitrary constant

$=-\frac{1}{5}\cos(x^5+6)+C$

Hope this answer is helpful.

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