Solve ∫ x^2sqrt{x wrt xquad2.int5

$$\int x ^ { 2 } \sqrt { x } d x \quad 2 . \int 5$$

Evaluate

$$x_{2}x^{\frac{5}{2}}+С$$

Solution Steps

Find the integral of x^{2}\sqrt{x} using the table of common integrals rule \int a\mathrm{d}x_{2}=ax_{2}.

$$x^{2}\sqrt{x}x_{2}$$

Simplify.

$$x^{\frac{5}{2}}x_{2}$$

If F\left(x_{2}\right) is an antiderivative of f\left(x_{2}\right), then the set of all antiderivatives of f\left(x_{2}\right) is given by F\left(x_{2}\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$x^{\frac{5}{2}}x_{2}+С$$

Differentiate w.r.t. x

$$\frac{5x_{2}x^{\frac{3}{2}}}{2}$$