Integral using Substitution (Simple Exponential Functions)

I = \int e^{\frac{9}{10} x + \frac{4}{3}} d x

Put

u = \frac{9}{10} x + \frac{4}{3}, then

d u = (\frac{9}{10}) d x

Or,

(\frac{10}{9}) d u = d x

So,

I = \int e^{u} (\frac{10}{9}) d u

Or,

I = \frac{10}{9} \int e^{u} d u

Or,

I = \frac{10}{9} e^{u} + C

Or,

I = \frac{10}{9} e^{\frac{9}{10} x + \frac{4}{3}} + C

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