Question

integrating exponential functions
x^4e^(x^5) dx

Answer 1

i kno wu=x^5

Answer 2

\[\int\limits x^4e^{x^5} dx\]
Let u =\[x^{5}\]

So, the integral is now: \[\int\limits x ^{4} e ^{u} dx\]
u=\[x^{5}\] so du=\[5x^{4} dx\] and dx=du/(5x^4)
Integral:
\[\int\limits x^{4} e^{u} dx/(5x^{4})\]
The x^4 factors cancel out, and you can pull the (1/5) outside of the integral. All you're left with now is \[1/5 \int\limits e^{u} du = (1/5)e^{u} + C\]
Plugging back in for u gives the answer as:
\[(1/5)e^{x^5}+C\]

Answer 3

x^4e^(x^5) dx
u = x^5 --> du/5 = x^4dx
= (1/5) Int e^u du = (1/5) e^(x^5) + C