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Calculus practice

Logarithmic and Exponential Integrals worksheets

Practice exact direct antiderivatives for multiples of 1/x, e^x, and integer-base exponential functions.

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Find each indefinite integral exactly. Include + C and state the real domain of the integrand.

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Choose the matching direct rule

Reciprocal integrands produce natural logarithms with absolute values. Natural-base exponentials stay unchanged, while integer-base exponentials require division by the natural logarithm of the base.

Learning objective

What this activity builds

Integrate reciprocal and exponential functions exactly, including absolute values, logarithmic base factors, constants of integration, and real domains.

Worked example

Find the integral of 3(2^x) dx.

3(2^x)/ln(2) + C, for all real x.

Because the derivative of 2^x is 2^x ln(2), divide by ln(2). Differentiation cancels that factor.

Teaching notes

Make the practice count

  • Use ln|x| for the reciprocal family so both nonzero intervals are represented.
  • Keep ln(n) exact for an integer base n.
  • Differentiate the result to check the coefficient and base factor.

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Math SheetNameScoreTeacherDateLogarithmic and Exponential IntegralsFind each indefinite integral exactly. Include + C and state the real domain of the integrand.1.-2·7xdx2.-7·exdx3.1xdx4.-4·3xdx5.-10xdx6.52·exdx7.9·exdx8.-12·3xdx9.10xdx10.-5xdxmath-sheet.comPage 1 of 1

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