Integrate 5 4 &#xFEFF; </mrow> e 6 x </mrow>

Alisa Durham

Alisa Durham

Answered question

2022-05-13

Integrate 5 4  e 6 x ( e 6 x 4 ) 5 with respect to x.

Answer & Explanation

kazneni3tr2b

kazneni3tr2b

Beginner2022-05-14Added 17 answers

Simplify.

5e6x(e6x-4)54dx

Since 54 is constant with respect to x, move 54 out of the integral.

54e6x(e6x-4)5dx

Let u2=e6x-4. Then du2=6e6xdx, so 16du2=e6xdx. Rewrite using u2 and du2.

54u2516du2

Combine u25 and 16.

54u256du2

Since 16 is constant with respect to u2, move 16 out of the integral.

54(16u25du2)

Simplify.

524u25du2

By the Power Rule, the integral of u25 with respect to u2 is 16u26.

524(16u26+C)

Simplify.

5144u26+C

Replace all occurrences of u2 with e6x-4.

5144(e6x-4)6+C

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