Integral using Substitution (Simple Exponential Functions)

I = \int e^{\frac{1}{4} x + \frac{8}{5}} d x

Put

u = \frac{1}{4} x + \frac{8}{5}, then

d u = (\frac{1}{4}) d x

Or,

(4) d u = d x

So,

I = \int e^{u} (4) d u

Or,

I = 4 \int e^{u} d u

Or,

I = 4 e^{u} + C

Or,

I = 4 e^{\frac{1}{4} x + \frac{8}{5}} + C

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