Solve ∫ 9sqrt[5]{x^4 wrt x

$$\int{ 9 \sqrt[ 5 ]{ { x }^{ 4 } } }d x$$

Evaluate

$$5x^{\frac{9}{5}}+С$$

Solution Steps

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

$$9\int x^{\frac{4}{5}}\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{\frac{4}{5}}\mathrm{d}x with \frac{5x^{\frac{9}{5}}}{9}. Multiply 9 times \frac{5x^{\frac{9}{5}}}{9}.

$$5x^{\frac{9}{5}}$$

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.

$$5x^{\frac{9}{5}}+С$$

Differentiate w.r.t. x

$$9x^{\frac{4}{5}}$$