Evaluate the following integrals. Include absolute values only when needed.

alesterp

alesterp

Answered question

2021-10-10

Evaluate the following integrals. Include absolute values only when needed.
0ln2e3xe3xe3x+e3x

Answer & Explanation

Benedict

Benedict

Skilled2021-10-11Added 108 answers

The given integral is 0ln2e3xe3xe3x+e3x
Evaluate as follows.
0ln2e3xe3xe3x+e3x=130ln23e3x3e3xe3x+e3xdx
=130ln2d(e3x+e3x)e3x+e3x
=13[ln(e3x+e3x)]0ln2
=13[ln(e3ln2+e3ln2)ln(e0+e0)]
=13[ln(23+23)ln(1+1)]
=13ln(22+232)
Thus, 0ln2e3xe3xe3x+e3x=13ln(22+232)

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