Solve ∫ (e^y-2) wrt y

$$\int ( e ^ { y } - 2 ) d y$$

Evaluate

$$С+e^{y}-2y$$

Solution Steps

Integrate the sum term by term.

$$\int e^{y}\mathrm{d}y+\int -2\mathrm{d}y$$

Use \int e^{y}\mathrm{d}y=e^{y} from the table of common integrals to obtain the result.

$$e^{y}+\int -2\mathrm{d}y$$

Find the integral of -2 using the table of common integrals rule \int a\mathrm{d}y=ay.

$$e^{y}-2y$$

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

$$e^{y}-2y+С$$

Differentiate w.r.t. y

$$e^{y}-2$$