حل ∫ 2x^2/3

$$\int \frac { 2 x ^ { 2 } } { 3 }$$

تقدير القيمة

$$\frac{2x^{3}}{9}+С$$

خطوات الحل

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

$$\frac{2}{3}\int x^{2}\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{2}\mathrm{d}x with \frac{x^{3}}{3}.

$$\frac{2}{3}\times \frac{x^{3}}{3}$$

تبسيط.

$$\frac{2x^{3}}{9}$$

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.

$$\frac{2x^{3}}{9}+С$$

تفاضل w.r.t. x

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