Integrate the cosine of an exponential expression

The video tutorial covers the substitution method in calculus, focusing on the chain rule for differentiation. It begins with an introduction to substitution, followed by a detailed explanation of the chain rule. The instructor demonstrates how to apply the chain rule in solving calculus problems, emphasizing the importance of understanding the derivative of the inside function. The tutorial concludes with an integration example using substitution, reinforcing the concepts discussed.

What is the first step in choosing a substitution for integration?

• Look at the numerator of a rational expression

• Choose a constant value

• Select any random function

• Consider the function inside another function

What is the chain rule used for in differentiation?

• To integrate functions

• To solve algebraic equations

• To find limits of functions

• To differentiate composite functions

When applying the chain rule, what must you remember to do?

• Add the derivative of the outer function

• Divide by the derivative of the outer function

• Multiply by the derivative of the inner function

• Subtract the derivative of the inner function

What is the integral of cosine in terms of 'u'?

• Cosine of u plus a constant

• Sine of u plus a constant

• Tangent of u plus a constant

• Secant of u plus a constant

After integrating, what is the final step in substitution?

• Multiply by a constant

• Differentiate the result

• Convert back to the original variable

• Leave the answer in terms of 'u'