Integrate − <mrow> 3 x 3 </mrow>

Matilda Webb

Matilda Webb

Answered question

2022-05-13

Integrate 3 x 3 2  + x 2 2 2 x + 3 sin ( 3 x ) with respect to x.

Answer & Explanation

necrologo9yh43

necrologo9yh43

Beginner2022-05-14Added 23 answers

Split the single integral into multiple integrals.

-3x32dx+x22dx+-2xdx+3sin(3x)dx

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

-3x32dx+x22dx+-2xdx+3sin(3x)dx

Since 32 is constant with respect to x, move 32 out of the integral.

-(32x3dx)+x22dx+-2xdx+3sin(3x)dx

By the Power Rule, the integral of x3 with respect to x is 14x4.

-32(14x4+C)+x22dx+-2xdx+3sin(3x)dx

Since 12 is constant with respect to x, move 12 out of the integral.

-32(14x4+C)+12x2dx+-2xdx+3sin(3x)dx

By the Power Rule, the integral of x2 with respect to x is 13x3.

-32(14x4+C)+12(13x3+C)+-2xdx+3sin(3x)dx

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

-32(14x4+C)+12(13x3+C)-2xdx+3sin(3x)dx

By the Power Rule, the integral of x with respect to x is 12x2.

-32(14x4+C)+12(13x3+C)-2(12x2+C)+3sin(3x)dx

Since 3 is constant with respect to x, move 3 out of the integral.

-32(14x4+C)+12(13x3+C)-2(12x2+C)+3sin(3x)dx

Let u=3x. Then du=3dx, so 13du=dx. Rewrite using u and du.

-32(14x4+C)+12(13x3+C)-2(12x2+C)+3sin(u)13du

Simplify.

-32(14x4+C)+12(13x3+C)-2(x22+C)+3sin(u)3du

Since 13 is constant with respect to u, move 13 out of the integral.

-32(14x4+C)+12(13x3+C)-2(x22+C)+3(13sin(u)du)

Simplify.

-32(14x4+C)+12(13x3+C)-2(x22+C)+sin(u)du

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

-32(14x4+C)+12(13x3+C)-2(x22+C)-cos(u)+C

Simplify.

-3x48+x36-x2-cos(u)+C

Replace all occurrences of u with 3x.

-3x48+x36-x2-cos(3x)+C

Reorder terms.

-38x4+16x3-x2-cos(3x)+C

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?