Question

integration

e^x/e^x+1 dx

Answer 1

\[\Large \int \frac{e^x}{e^x+1}dx \]
That?
If yes, then use the u Substitution method for

\[\Large u=e^x+1 \]

Answer 2

\[\int\limits_{}^{} \frac{e^{x}}{e ^{x}+1 }\] but u=\[e ^{x}\]

Answer 3

Easier to let u = e^x + 1

Answer 4

You don't want to do a u=e^x substitution, this turns out to be redundant, so as I suggested u=e^x+1 will do you better.

Answer 5

okay.. i will try u=e^x+1

Answer 6

\[\Huge \checkmark \]

Answer 7

then if \[x ^{3} \sqrt{x ^{2}+3}\] which is u please explain to me

Answer 8

x^3 (x^2+3)^1/2

Answer 9

\[\Large \int x^3\sqrt{x^2+3}dx \]
If

\[ \Large u=x^2+3 \]
Then
\[\Large x=\sqrt{u-3} \]
So best might be using various substitutions:
\[\Large dx=\frac{1}{2\sqrt{u-3}}du \]
Maybe this will help you since the integral then becomes:

\[\Large \int\sqrt{u-3}^3 \cdot \sqrt{u} \cdot \frac{1}{2\sqrt{u-3}}du \]

Answer 10

If I didn't make any careless mistakes, then this will simplify to:
\[\Large \frac{1}{2} \int (u-2)\cdot u^{1/2}du \]

Answer 11

Sorry should be u-3

Answer 12

Strange substitution at first, if you have any questions mention it to me @arifadli8