Question

Evaluate the definite integral (limits from 0 to 1) using substitution.

x^13*(e^x^14) dx

My question is which do you substitute?

Answer 1

u = x^14

Answer 2

ok so using u=x^14, i get
\[1\div14\] \[\int\limits_{0}^{1}\] then x^13*e^(-u) du

is the next step to evaluate using the limits?

Answer 3

i cant seem to get all of the equation to be on the same line..anyways the 1/14 i isolated in front of the integral sign

Answer 4

\[\int x^{13}e^{x^{14} }dx\]

Answer 5

\[u=x^{14}\]
\[du=14x^{13}dx\]
\[\frac{du}{14}=x^{13}dx\]

\[\int x^{13}e^{x^{14}}dx=\int e^{x^{14}}x^{13}dx=\int \frac{e^u}{14}du=\frac{1}{14}\int e^u du \]

Answer 6

\[\int e^u=e^u+c\]

\[\frac{1}{14}\int e^u du=\frac{1}{14}e^u+c=\frac{1}{14} e^{x^{14}}+c\]

Answer 7

ok thank you i understand now :)