Indefinite Integral of x divided by the square root of 1 minus x squared

The video tutorial explains how to find the indefinite integral of x divided by the square root of 1 minus x squared using u-substitution. The process involves defining u and du, simplifying the integral, applying the power rule, and finalizing the solution to arrive at the answer: negative square root of 1 minus x squared plus a constant.

What is the first step recommended to solve the integral of x divided by the square root of 1 minus x squared?

• Use partial fraction decomposition

• Use u-substitution

• Use integration by parts

• Use trigonometric substitution

In the u-substitution method, what is u set equal to?

• x divided by 1 minus x squared

• x squared

• 1 plus x squared

• 1 minus x squared

What is the expression for du when u is equal to 1 minus x squared?

• -x dx

• x dx

• -2x dx

• 2x dx

After substituting u and dx, what constant is moved outside the integral?

• 1/2

• -1/2

• 2

• -2

What is the integral of u to the power of -1/2 with respect to u?

• u to the power of 3/2

• u to the power of -1/2

• u to the power of -3/2

• u to the power of 1/2

What is the result of negative one-half plus one in the integration process?

• One-half

• One

• Negative one-half

• Zero

What is the purpose of using the power rule in this integration problem?

• To differentiate the function

• To simplify the expression

• To find the antiderivative

• To solve for x

What is the power rule for integration used in this problem?

• Integral of x to the n dx is x to the n minus 1 over n plus 1 plus c

• Integral of x to the n dx is x to the n minus 1 over n minus 1 plus c

• Integral of x to the n dx is x to the n plus 1 over n plus 1 plus c

• Integral of x to the n dx is x to the n plus 1 over n minus 1 plus c

What is the final expression for the indefinite integral after replacing u with the original expression?

• Negative square root of x squared plus c

• Negative square root of 1 plus x squared plus c

• Negative square root of x plus c

• Negative square root of 1 minus x squared plus c

What is the final step in solving the indefinite integral in this problem?

• Finding the derivative

• Replacing u with the original expression

• Simplifying the expression

• Applying the power rule