Solve ∫ sqrt{(5e^2t)^2}

$$\int \sqrt { ( 5 e ^ { 2 t } ) ^ { 2 } }$$

Evaluate

$$5xe^{2t}+С$$

Solution Steps

Find the integral of \sqrt{\left(5e^{2t}\right)^{2}} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\sqrt{\left(5e^{2t}\right)^{2}}x$$

Simplify.

$$5e^{2t}x$$

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.

$$5e^{2t}x+С$$

Differentiate w.r.t. x

$$5e^{2t}$$