Solve ∫ sqrt{11/25}+3sqrt{71/9}-0.6sqrt{3025}

$$\int \sqrt { \frac { 11 } { 25 } } + 3 \sqrt { \frac { 71 } { 9 } } - 0.6 \sqrt { 3025 }$$

Evaluate

$$\frac{\left(\sqrt{11}+5\sqrt{71}-165\right)x}{5}+С$$

Solution Steps

Find the integral of \frac{\sqrt{275}}{25}+\frac{\sqrt{639}}{3}-\frac{3\sqrt{3025}}{5} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\left(\frac{\sqrt{275}}{25}+\frac{\sqrt{639}}{3}-\frac{3\sqrt{3025}}{5}\right)x$$

Simplify.

$$\left(\frac{\sqrt{11}}{5}+\sqrt{71}-33\right)x$$

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.

$$\left(\frac{\sqrt{11}}{5}+\sqrt{71}-33\right)x+С$$

Differentiate w.r.t. x

$$\frac{\sqrt{11}}{5} + \sqrt{71} - 33 = -23.910525269$$