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Here is the problem: integrate 3 to the power x.

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Find the indefinite integral (antiderivative) of 3 to the power x with respect to x.

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Start with the integral.

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Exponential rule: the integral of aᵘ du equals aᵘ/ln a.

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Simplify and add the constant of integration.

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So the answer is 3 to the power x / ln(3) plus C.

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An antiderivative F satisfies F prime of x equals f(x). Because the derivative of any constant is 0, every antiderivative differs by a constant C.

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Differentiated the answer and compared it with the integrand at 8 sample points, which checks out.