Question

Can someone help walk me through some u substitution problems?

Answer 1

sure

Answer 2

\[\int\limits_{}^{} \frac{ e ^{x} }{ e ^{x}+1 } dx\]

Answer 3

\[\int\limits_{}^{} \cos(\theta)\sin ^{6}(\theta)d \theta \]

Answer 4

Would the first one be \[-\frac{ 1 }{ (e ^{x}+1)^{2} }\]

Answer 5

For the second one..
\[u = \sin(\theta), du = \cos(\theta)d \theta \]

Answer 6

and yes for the first one you're correct

Answer 7

For second one once you have the sub:
\[\int\limits_{}^{}u^6du\]
and it's easy from there.

Answer 8

\[6\sin ^{5}\theta +c\] ?

Answer 9

Remember you're integrating not taking the derivative

Answer 10

Ohhhhh, so would the first one be wrong then since I took the derivative?

Answer 11

ln(e^(x)+1)+c?

Answer 12

and the second one would be \[\frac{ \sin^{7}\theta}{ 7 }\] ?