5 Steps to a 5 AP Calculus BC 2019

212 STEP 4. Review the Knowledge You Need to Score High

Example 9

Evaluate

∫

sinx− 1

cos

dx.

Rewrite

∫(

sinx

cosx

−

1

cosx

)

dx=

∫

(tanx −secx)dx=

∫

tanxdx−

∫

secxdx

=ln

∣∣

secx

∣∣

−ln

∣∣

secx+tanx

∣∣

+C=ln

∣

∣∣

∣

secx

secx+tanx

∣

∣∣

∣+C

or−ln

∣∣

sinx+ 1

∣∣

+C.

Example 10

Evaluate

∫

e^2 x

ex

dx.

Rewrite the integral as

∫

exdx=ex+C.

Example 11

Evaluate

∫

3

1 +x^2

dx.

Rewrite as 3

∫

1

1 +x^2

dx=3 tan−^1 x+C.

Example 12

Evaluate

∫

1

√

9 −x^2

dx.

Rewrite as

∫

1

√

32 −x^2

dx=sin−^1

(

x

3

)

+C.

Example 13

Evaluate

∫

7 xdx.

∫

7 xdx=

7 x

ln 7

+C

KEY IDEA

Reminder: You can always check the result by taking the derivative of the answer.

TIP • Be familiar with the instructions for the different parts of the exam before the day of

exam. Review the instructions in the practice tests provided at the end of this book.