Integral using Substitution (Complex Exponential Functions)

I = \int e^{3 x^{2} + 4 x - 1} (3 x + 2) d x

Put

u = 3 x^{2} + 4 x - 1

, then

d u = (6 x + 4) d x

Or,

\frac{1}{2} d u = (3 x + 2) d x

So,

I = \int e^{u} (\frac{1}{2}) d u

Or,

I = \frac{1}{2} \int e^{u} d u

Or,

I = \frac{1}{2} e^{u} + C

Or,

I = \frac{1}{2} e^{3 x^{2} + 4 x - 1} + C

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