Find the Integral Using the Indicated Substitution $$\int \tan ^ { 2 } x \sec ^ { 2 } x d x , \quad u = \tan x$$

question 48

Multiple Choice

Find the integral using the indicated substitution.
$$\int \tan ^ { 2 } x \sec ^ { 2 } x d x , \quad u = \tan x$$
Select the correct answer.

• A) \(\frac { 1 } { 8 } \tan ^ { 8 } x \sec ^ { 2 } x + C\)
• B) \(\frac { 1 } { 8 } \tan ^ { 8 } x \sec ^ { 3 } x + C\)
• C) \(\frac { 1 } { 24 } \tan ^ { 8 } x \sec ^ { 3 } x + C\)
• D) \(\frac { 1 } { 8 } \tan ^ { 8 } x + C\)

---

Definitions:

Brake Drums

Components of a drum brake system which rotate with the wheel and where the brake shoes press against to stop the vehicle.

Reconditioning

The process of repairing, restoring, or otherwise returning a used or worn product to a good, usable condition, often involving replacing parts and a thorough cleaning.

Heat Checked

A term describing the presence of surface cracks on a component, such as a brake disc, caused by repeated heating and cooling cycles.

Governor Cutout Pressure

The pressure at which a compressor’s governor stops the compressor from building air, thereby preventing over-pressurization in a pneumatic system.