What is &#x222B;<!-- ∫ --> 5 7 </mfrac> <mrow class="MJX-TeXAtom-ORD"> &#xFEFF

kazue72949lard

kazue72949lard

Answered question

2022-04-04

What is 5 7  x 2 cos ( x ) d x?

Answer & Explanation

Braeden Shannon

Braeden Shannon

Beginner2022-04-05Added 13 answers

Simplify.

5x2cos(x)7dx

Since 57 is constant with respect to x, move 57 out of the integral.

57x2cos(x)dx

Integrate by parts using the formula udv=uv-vdu, whereu=x2 and dv=cos(x).

57(x2sin(x)-sin(x)(2x)dx)

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

57(x2sin(x)-(2sin(x)(x)dx))

Multiply 2 by -1.

57(x2sin(x)-2sin(x)(x)dx)

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

57(x2sin(x)-2(x(-cos(x))--cos(x)dx))

Since -1 is constant with respect to x, move -1 out of the integral.

57(x2sin(x)-2(x(-cos(x))--cos(x)dx))

Simplify.

57(x2sin(x)-2(x(-cos(x))+cos(x)dx))

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

57(x2sin(x)-2(x(-cos(x))+sin(x)+C))

Rewrite 57(x2sin(x)-2(x(-cos(x))+sin(x)+C)) as 57(x2sin(x)+2xcos(x)-2sin(x))+C.

57(x2sin(x)+2xcos(x)-2sin(x))+C

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