Antiderivatives of Exponential and Logarithmic Functions Quiz

What is the antiderivative of an exponential function of the form a^x?

• a^x / ln(a) + C

• a^x ln(a) + C

• a^x + C

• ln(a^x) + C

Which of the following is the correct formula for the antiderivative of e^x?

• ln(e^x) + C

• e^x + C

• e^x ln(e) + C

• e^x / ln(e) + C

What is the integration formula for logarithmic functions?

• x log_b(xe) + C

• log_b(x) + C

• log_b(x) / x + C

• x / log_b(x) + C

What is the antiderivative of log_2(x)?

• x log_2(xe) + C

• log_2(x) + C

• x / log_2(x) + C

• log_2(x) / x + C

Which of the following is true about the constant of integration?

• It is always zero.

• It can be any real number.

• It must be a positive number.

• It is always one.

What is the result of ∫ 2^x dx?

• 2^x + C

• 2^x / ln(2) + C

• 2^x ln(2) + C

• ln(2^x) + C

What is the antiderivative of 5e^x?

• 5e^x ln(e) + C

• 5e^x + C

• 5e^x / ln(e) + C

• e^x + C

Which theorem allows us to take constants outside the integral?

• Sum Rule

• Product Rule

• Constant Multiple Theorem

• Difference Rule

What is the antiderivative of log_4(x^2)?

• 2 log_4(x) + C

• log_4(x^2) + C

• x log_4(x) + C

• 2x log_4(xe) + C

What is the result of ∫ (2^x + 1) dx?

• 2^x ln(2) + x + C

• 2^x + x + C

• ln(2^x) + x + C

• 2^x / ln(2) + x + C