Integration by Parts

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A company's profit rate is modeled by $p(t) = \ln t$ million dollars per year, where $t$ is time in years. Find the total profit accumulated from $t=1$ to $t=e$ years.

A.0

B.1

e

e-1

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Evaluate the indefinite integral: $\int (3x^2+1) e^{2x} \, dx$ .

\frac{1}{4}(6x^2 + 6x - 1)e^{2x} + C

\frac{1}{4}(6x^2 - 6x + 5)e^{2x} + C

\frac{1}{2}(6x^2 - 6x + 5)e^{2x} + C

\frac{1}{4}(6x^2 - 2x + 3)e^{2x} + C

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Evaluate the indefinite integral $\int x^2 e^{3x} \, dx$ .

\frac{1}{3}x^2 e^{3x} - \frac{2}{9}x e^{3x} + \frac{2}{9}e^{3x} + C

\frac{1}{27}(9x^2 - 6x + 2)e^{3x} + C

\frac{1}{3}x^2 e^{3x} - \frac{2}{3}x e^{3x} + \frac{2}{3}e^{3x} + C

\frac{1}{3}x^2 e^{3x} - \frac{2}{9}x e^{3x} + \frac{1}{9}e^{3x} + C

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Integration by Parts

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