What is &#x222B;<!-- ∫ --> 4 3 </mfrac> <mrow class="MJX-TeXAtom-ORD"> &#xFEFF

lifretatox8n

lifretatox8n

Answered question

2022-04-04

What is 4 3  x 2 sin ( x ) d x?

Answer & Explanation

recajossikpfmq

recajossikpfmq

Beginner2022-04-05Added 19 answers

Simplify.

4x2sin(x)3dx

Since 43 is constant with respect to x, move 43 out of the integral.

43x2sin(x)dx

Integrate by parts using the formula udv=uv-vdu, where u=x2 and dv=sin(x).

43(x2(-cos(x))--cos(x)(2x)dx)

Multiply 2 by -1.

43(x2(-cos(x))--2cos(x)xdx)

Since -2 is constant with respect to x, move -2 out of the integral.

43(x2(-cos(x))-(-2cos(x)xdx))

Multiply -2 by -1.

43(x2(-cos(x))+2cos(x)xdx)

Integrate by parts using the formula udv=uv-vdu, where u=x and dv=cos(x).

43(x2(-cos(x))+2(xsin(x)-sin(x)dx))

The integral of sin(x) with respect to x is -cos(x).

43(x2(-cos(x))+2(xsin(x)-(-cos(x)+C)))

Rewrite 43(x2(-cos(x))+2(xsin(x)-(-cos(x)+C))) as 43(-x2cos(x)+2xsin(x)+2cos(x))+C.

43(-x2cos(x)+2xsin(x)+2cos(x))+C

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