Use u substitution with trigonometric functions

The video tutorial explains how to solve an integral involving the tangent function by using U substitution. It begins by identifying the derivative of tangent as secant squared, then defines U as tangent of X and DU as secant squared of X DX. The integral is rewritten in terms of U and DU, and the solution is found by integrating U squared DU, resulting in U cubed divided by three plus C. The integral is then plugged back in to complete the solution.

What is the derivative of the tangent function?

• Secant squared

• Sine squared

• Cosecant squared

• Cosine squared

In the substitution process, what is U set to?

• Sine of X

• Cosine of X

• Tangent of X

• Secant of X

What is the expression for du in terms of X?

• Secant squared of X times DX

• Cosine squared of X times DX

• Tangent squared of X times DX

• Sine squared of X times DX

What is the integral of U squared with respect to U?

• U squared divided by 2 plus C

• U cubed divided by 3 plus C

• U to the fourth divided by 4 plus C

• U to the fifth divided by 5 plus C

What is added to the result of the integration to complete the solution?

• A derivative term

• A variable of integration

• A constant of integration

• A substitution term