Question #14a63

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Answer 1 · 2018-01-30T08:43:53

#1/(ln(3)+2)e^((ln(3)+2)x)+C#

We want to solve

#int3^x*e^(2x)dx#

Rewrite the integrand

#inte^(x*ln(3))*e^(2x)dx#

#inte^((ln(3)+2)x)dx#

Use substitution
Let #u=(ln(3)+2)x# then #(du)/dx=ln(3)+2#

#int1/(ln(3)+2)e^udu#

Integrate

#1/(ln(3)+2)e^u+C#

Substitute #u=(ln(3)+2)x#

#1/(ln(3)+2)e^((ln(3)+2)x)+C#

Or

#1/(ln(3)+2)*3^x*e^(2x)+C#