Solve ∫ t^12dt=

$$\int t ^ { 12 } d t =$$

Evaluate

$$\frac{t^{13}}{13}+С$$

Solution Steps

Since \int t^{k}\mathrm{d}t=\frac{t^{k+1}}{k+1} for k\neq -1, replace \int t^{12}\mathrm{d}t with \frac{t^{13}}{13}.

$$\frac{t^{13}}{13}$$

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

$$\frac{t^{13}}{13}+С$$

Differentiate w.r.t. t

$$t^{12}$$