Cracking The Ap Calculus ab Exam 2018

Now you can integrate.

PROBLEM 5. Evaluate

Answer: Let u = x^3 − 1 and du = 3x^2 dx, and substitute.

∫

Now integrate.

ln  |u| +   C

And substitute back.

ln  |x^3    −   1|  +   C

PROBLEM 6. Evaluate ∫e^5 x dx.

Answer: Let u = 5x and du = 5dx. Then du = dx. Substitute in.

∫e

u   du

Integrate.

eu  +   C

And substitute back.

e^5 x   +   C

PROBLEM 7. Evaluate ∫ 23 x dx.

Answer: Let u = 3x and du = 3dx. Then du = dx. Make the substitution.