Indefinite Integral of 7 Raised to the Natural Log of X

The video tutorial explains how to find the indefinite integral of 7 raised to the natural log of X. It begins by rewriting the expression using exponent rules, then applies the power rule for integration. The tutorial concludes with the final expression and a brief explanation of the solution.

What is the first step in solving the indefinite integral of 7 raised to the natural log of X?

• Integrate directly

• Switch the exponents

• Replace 7 with e raised to the ln 7

• Use the power rule directly

What is the base of the natural logarithm?

• e

• 7

• 10

• 2

Why can exponents be switched in the expression e raised to the natural log of x raised to the natural log of 7?

• Because they are constants

• Because they are equal

• Because exponents can be multiplied

• Because the base is e

What is the result of e raised to the ln 7?

• 1

• 7

• e

• ln 7

What is the simplified form of e raised to the natural log of x raised to the natural log of 7?

• x raised to the natural log of 7

• x raised to the 7

• 7 raised to the natural log of x

• e raised to the x

What rule is used to find the antiderivative of a variable raised to a constant?

• Quotient rule

• Product rule

• Chain rule

• Power rule

How is the expression x raised to the natural log of 7 split into two parts?

• As a sum of two terms

• As a product of two expressions

• As a difference of two terms

• As a quotient of two expressions

What is the equivalent expression for x raised to the ln 7?

• 7 raised to the ln x

• x raised to the 7

• ln 7 raised to the x

• 7 raised to the x

What is the final form of the indefinite integral of 7 raised to the natural log of X?

• 7 times X raised to the ln X plus C

• X raised to the ln 7 times 7 plus C

• X raised to the 7 divided by ln 7 plus C

• 7 raised to the natural log of X times X divided by 1 plus the natural log of 7 plus C

What is the constant of integration added to the antiderivative?

• C

• K

• L

• M