U-substitution for indefinite integrals

How do you u-substitute?

1. Find u (u is WHATEVER is in e, parentheses, power, etc, anything inside anything)

2. Find du (du is is derivative of whatever you found for u

3. Substitute once EVERYTHING in the equation has been substituted for u or du

4. Solve the integral with the u and du (IMPORANT: du VANISHES when solving for integrals, do not worry about it) + ALWAYS ADD A +C, NEVER FORGET THE +C FOR INDEFINITE INTEGRALS!!!!

5. replace everything back from u to the original variable/numbers

NOTE: you might have to rearrange the u and du equations before substituting so that every number is substituted (see image for details)

…that’s it

ok

there’s literally nothing else

ok

When do you use u-substitution?

1. when one function is inside another function

2. there’s like a big power

3. there is more than 1 of the variable in the integral

How do you find the integral using u-sub if the integral is something where it’s hard to find the u, like sec²xtan³x?

find a hidden derivative

ex) d/dx sec²x = tanx

therefore u=tanx