Solve ∫ e^3tdtau

$$\int e ^ { 3 t } d \tau$$

Evaluate

$$\tau e^{3t}+С$$

Solution Steps

Find the integral of e^{3t} using the table of common integrals rule \int a\mathrm{d}\tau =a\tau .

$$e^{3t}\tau$$

If F\left(\tau \right) is an antiderivative of f\left(\tau \right), then the set of all antiderivatives of f\left(\tau \right) is given by F\left(\tau \right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$e^{3t}\tau +С$$

Differentiate w.r.t. t

$$3\tau e^{3t}$$