Solve ∫ (1-t^-052)dt

$$\int ( 1 - t ^ { - 052 } ) d t$$

Evaluate

$$С$$

Solution Steps

Multiply 0 and 52 to get 0.

$$\int 1-t^{0}\mathrm{d}t$$

Calculate t to the power of 0 and get 1.

$$\int 1-1\mathrm{d}t$$

Subtract 1 from 1 to get 0.

$$\int 0\mathrm{d}t$$

Find the integral of 0 using the table of common integrals rule \int a\mathrm{d}t=at.

$$0$$

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.

$$С$$

Differentiate w.r.t. t

$$0$$