Antiderivatives and Substitution Techniques

The video tutorial explains how to determine the antiderivative using the substitution method. It begins by setting u = 7x and finding the differential. The integral is adjusted by replacing dx with 1/7du and factoring out constants. The tutorial then integrates e^u with respect to u and substitutes back to express the antiderivative in terms of x. The video concludes with a brief mention of the next example to be covered.

What substitution is chosen for u in the given problem?

• u = x

• u = 7x

• u = x^2

• u = 2x

What is the differential du in terms of dx?

• du = 7dx

• du = 2dx

• du = dx

• du = 1/7dx

How is dx replaced in the integral after substitution?

• dx is replaced with du

• dx is replaced with 2du

• dx is replaced with 7du

• dx is replaced with 1/7du

What constant is factored out of the integral after substitution?

• 1/2

• 1/7

• 2

• 7

What is the antiderivative of e^u with respect to u?

• e^u + C

• u^2/2 + C

• ln|u| + C

• 1/u + C

What is the final antiderivative in terms of x?

• 2/7 e^x + C

• 2/7 e^(7x) + C

• 7/2 e^(2x) + C

• e^(7x) + C