Compute − 2 x 3 </mrow> − x 2 </mrow

Leon Robinson

Leon Robinson

Answered question

2022-05-11

Compute ( 2 x 3 x 2 + 3 2 x 2 + 3 sin ( x ) )  d x.

Answer & Explanation

Corinne Choi

Corinne Choi

Beginner2022-05-12Added 15 answers

Remove parentheses.

-2x3-x2+32x2+3sin(x)dx

Split the single integral into multiple integrals.

-2x3dx+-x2dx+32x2dx+3sin(x)dx

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

-2x3dx+-x2dx+32x2dx+3sin(x)dx

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

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

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

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

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

-2(14x4+C)-(13x3+C)+32x2dx+3sin(x)dx

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

-2(14x4+C)-(13x3+C)+321x2dx+3sin(x)dx

Simplify the expression.

-2(x44+C)-(x33+C)+32x-2dx+3sin(x)dx

By the Power Rule, the integral of x-2 with respect to x is -x-1.

-2(x44+C)-(x33+C)+32(-x-1+C)+3sin(x)dx

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

-2(x44+C)-(x33+C)+32(-x-1+C)+3sin(x)dx

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

-2(x44+C)-(x33+C)+32(-x-1+C)+3(-cos(x)+C)

Simplify.

-x42-x33-32x-3cos(x)+C

Reorder terms.

-12x4-13x3-32x-3cos(x)+C

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