Integral using Substitution (Complex Exponential Functions)

I = \int e^{3 x^{4} - 32 x^{3} - 6 x^{2} - 48 x + 6} (x^{3} - 8 x^{2} - x - 4) d x

Put

u = 3 x^{4} - 32 x^{3} - 6 x^{2} - 48 x + 6

, then

d u = (12 x^{3} - 96 x^{2} - 12 x - 48) d x

Or,

\frac{1}{12} d u = (x^{3} - 8 x^{2} - x - 4) d x

So,

I = \int e^{u} (\frac{1}{12}) d u

Or,

I = \frac{1}{12} \int e^{u} d u

Or,

I = \frac{1}{12} e^{u} + C

Or,

I = \frac{1}{12} e^{3 x^{4} - 32 x^{3} - 6 x^{2} - 48 x + 6} + C

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