Solve ∫ 50e^005tdt

$$\int 50 e ^ { 005 t } d t$$

Evaluate

$$50t+С$$

Solution Steps

Multiply 0 and 0 to get 0.

$$\int 50e^{0\times 5t}\mathrm{d}t$$

Multiply 0 and 5 to get 0.

$$\int 50e^{0t}\mathrm{d}t$$

Anything times zero gives zero.

$$\int 50e^{0}\mathrm{d}t$$

Calculate e to the power of 0 and get 1.

$$\int 50\times 1\mathrm{d}t$$

Multiply 50 and 1 to get 50.

$$\int 50\mathrm{d}t$$

Find the integral of 50 using the table of common integrals rule \int a\mathrm{d}t=at.

$$50t$$

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.

$$50t+С$$

Differentiate w.r.t. t

$$50$$