Integral using Substitution (Complex Exponential Functions)

I = \int e^{6 x^{5} + 45 x^{4} + 20 x^{3} + 135 x^{2} + 300 x - 30} (x^{4} + 6 x^{3} + 2 x^{2} + 9 x + 10) d x

Put

u = 6 x^{5} + 45 x^{4} + 20 x^{3} + 135 x^{2} + 300 x - 30

, then

d u = (30 x^{4} + 180 x^{3} + 60 x^{2} + 270 x + 300) d x

Or,

\frac{1}{30} d u = (x^{4} + 6 x^{3} + 2 x^{2} + 9 x + 10) d x

So,

I = \int e^{u} (\frac{1}{30}) d u

Or,

I = \frac{1}{30} \int e^{u} d u

Or,

I = \frac{1}{30} e^{u} + C

Or,

I = \frac{1}{30} e^{6 x^{5} + 45 x^{4} + 20 x^{3} + 135 x^{2} + 300 x - 30} + C

Algebra Analytic Geometry Differential Calculus Integral Calculus Home

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