Find the integral of 2 e <mrow class="MJX-TeXAtom-ORD">

Autumn Pham

Autumn Pham

Answered question

2022-05-05

Find the integral of 2 e x x 2 7 with respect to x.

Answer & Explanation

cartonarepcpo4

cartonarepcpo4

Beginner2022-05-06Added 12 answers

Since 27 is constant with respect to x, move 27 out of the integral.

27exx2dx

Integrate by parts using the formula udv=uv-vdu, where u=x2 and dv=ex.

27(x2ex-ex(2x)dx)

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

27(x2ex-(2ex(x)dx))

Multiply 2 by -1.

27(x2ex-2ex(x)dx)

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

27(x2ex-2(xex-exdx))

The integral of ex with respect to x is ex.

27(x2ex-2(xex-(ex+C)))

Rewrite 27(x2ex-2(xex-(ex+C))) as 27(x2ex-2xex+2ex)+C.

27(x2ex-2xex+2ex)+C

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