Cracking The Ap Calculus ab Exam 2018

As with the natural logarithm, most of these integrals use u-substitution.

Example 14: Find ∫e^7 x dx.

Let u = 7x, du = 7dx, and du = dx. Then you have

∫e

7 x dx  =   

∫e

u du    =    eu +   C

Substituting back, you get

e^7 x   +   C

In fact, whenever you see ∫ekx dx, where k is a constant, the integral is

∫e

kx  dx  =       +   C

Example 15: Find dx.

Let u = 3x^2 + 1, du = 6x dx, and du = x dx. The result is

Now it’s time to put the x’s back in.

Example 16: Find ∫esin x cos x dx.

Let u = sin x and du = cos x dx. The substitution here couldn’t be simpler.

∫^ e

u   du  =   eu  +   C   =   esin    x   +   C