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sattari [20]
4 years ago
5

20 POINTS ! Evaluate ∫ e3x cosh 2x dx

Mathematics
1 answer:
3241004551 [841]4 years ago
5 0
Question:
Evaluate \int{e^{3x}cosh(2x)dx

Solution:
substitute the identity 
cosh(2x)=\frac{e^{2x}+e^{-2x}}{2}
into integral
I=\int{e^{3x}cosh(2x)dx}
=\int{e^{3x}\frac{e^{2x}+e^{-2x}}{2}dx}
=\int\frac{e^{3x+2x}}{2}+\frac{e^{3x-2x}}{2}dx
=\int\frac{e^{5x}}{2}+\frac{e^{x}}{2}dx
=\frac{e^{5x}}{2*5}+\frac{e^{x}}{2}+C
=\frac{e^{5x}}{10}+\frac{e^{x}}{2}+C

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