Solve ∫ 2^2-3(2/5)^-2

$$\int 2 ^ { 2 } - 3 ( \frac { 2 } { 5 } ) ^ { - 2 }$$

Evaluate

$$-\frac{59x}{4}+С$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\int 4-3\times \left(\frac{2}{5}\right)^{-2}\mathrm{d}x$$

Calculate \frac{2}{5} to the power of -2 and get \frac{25}{4}.

$$\int 4-3\times \frac{25}{4}\mathrm{d}x$$

Multiply 3 and \frac{25}{4} to get \frac{75}{4}.

$$\int 4-\frac{75}{4}\mathrm{d}x$$

Subtract \frac{75}{4} from 4 to get -\frac{59}{4}.

$$\int -\frac{59}{4}\mathrm{d}x$$

Find the integral of -\frac{59}{4} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$-\frac{59x}{4}$$

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

$$-\frac{59x}{4}+С$$

Differentiate w.r.t. x

$$-\frac{59}{4} = -14\frac{3}{4} = -14.75$$