integrating by substitution C3 HELP

right so this one question has been ending me and idk wat is going on:



so getting dx in terms of du so we can make the substitution im left with:

to get it in terms of u we can sub u-4 into the e^2x because:

if you sub this back in and simplify i end up with


I honestly don't know what to do next. any help would be appreaciated!!

the answer is:

Factorise and use partial fractions.

right so this one question has been ending me and idk wat is going on:



so getting dx in terms of du so we can make the substitution im left with:

to get it in terms of u we can sub u-4 into the e^2x because:

if you sub this back in and simplify i end up with


I honestly don't know what to do next. any help would be appreaciated!!

the answer is:

Factorise and use partial fractions.

You're on the right track. Try partial fractions.
$\displaystyle \frac 1 {u^2-4u} \equiv \frac 1 {u(u-4)} \equiv \frac A u + \frac B {u-4}$
Where $A, B$ are constants to be determined.