What is the integral of #e^(0.5x)#?

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Answer 1 · 2018-07-18T14:01:08

#2e^{0.5x}+C#

#\int e^{0.5x}\ dx#

#=\int e^{0.5x}1/0.5d(0.5x)#

#=1/0.5\int e^{0.5 x}\ d(0.5x)#

#=2e^{0.5x}+C#

Answer 2 · 2018-07-18T14:05:18

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

Substiting #t=1/2x# we get

#x=2t# so #dx=2dt# and our integral is given by #2int e^tdt=2e^t+C=2e^(1/2x)+C#