Solve ∫ 4sqrt[5]{x wrt x

$$\int{ 4 \sqrt[ 5 ]{ x } }d x$$

Evaluate

$$\frac{10x^{\frac{6}{5}}}{3}+С$$

Solution Steps

Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.

$$4\int \sqrt[5]{x}\mathrm{d}x$$

Rewrite \sqrt[5]{x} as x^{\frac{1}{5}}. Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{\frac{1}{5}}\mathrm{d}x with \frac{x^{\frac{6}{5}}}{\frac{6}{5}}. Simplify. Multiply 4 times \frac{5x^{\frac{6}{5}}}{6}.

$$\frac{10x^{\frac{6}{5}}}{3}$$

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.

$$\frac{10x^{\frac{6}{5}}}{3}+С$$

Differentiate w.r.t. x

$$4\sqrt[5]{x}$$