Integration of Secant Cubed X

This video tutorial explains how to integrate secant cubed X using integration by parts. It begins by breaking down the integral into manageable parts and applying the integration by parts formula. The tutorial then simplifies the integral using trigonometric identities and focuses on integrating secant X through u-substitution. Finally, the solution is finalized by combining all parts to arrive at the integral of secant cubed X.

What is the first step in integrating secant cubed X?

• Use substitution method

• Use partial fraction decomposition

• Split into secant X and secant squared X

• Directly integrate secant cubed X

In integration by parts, what is chosen as the 'U' variable?

• Secant squared X

• Secant X

• DX

• Tangent X

What identity is used to replace tangent squared X?

• Cotangent squared X minus one

• Sine squared X plus one

• Cosine squared X plus one

• Secant squared X minus one

What is the integral of secant squared X?

• Cosecant X

• Secant X

• Cotangent X

• Tangent X

What is the purpose of multiplying by secant X plus tangent X in the integration process?

• To eliminate secant X

• To find the derivative

• To change the variable

• To simplify the integral

What substitution is made for the integration of secant X?

• U equals secant X plus tangent X

• U equals tangent X

• U equals secant squared X

• U equals secant X

What is the integral of 1 over U?

• Cosine X

• Tangent X

• Natural log of U

• Secant X

What is the final expression for the integral of secant cubed X?

• 1/2 times tangent X plus secant X plus C

• Tangent X plus secant X plus C

• Secant X plus tangent X plus C

• 1/2 times secant X tangent X plus natural log of secant X plus tangent X plus C

What operation is performed to both sides to obtain the final answer?

• Subtract 1

• Add 1

• Divide by 2

• Multiply by 2

What is the constant of integration denoted by?

• D

• C

• B

• A