Integral using Substitution (Simple Exponential Functions)

I = \int e^{\frac{2}{5} x + \frac{9}{4}} d x

Put

u = \frac{2}{5} x + \frac{9}{4}, then

d u = (\frac{2}{5}) d x

Or,

(\frac{5}{2}) d u = d x

So,

I = \int e^{u} (\frac{5}{2}) d u

Or,

I = \frac{5}{2} \int e^{u} d u

Or,

I = \frac{5}{2} e^{u} + C

Or,

I = \frac{5}{2} e^{\frac{2}{5} x + \frac{9}{4}} + C

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Copyright © Dayal D. Purohit, Ph.D.(Mathematics)