حل ∫ sqrt{x wrt x

$$\int{ \sqrt{ x } }d x$$

تقدير القيمة

$$\frac{2x^{\frac{3}{2}}}{3}+С$$

خطوات الحل

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

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

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.

$$\frac{2x^{\frac{3}{2}}}{3}+С$$

تفاضل w.r.t. x

$$\sqrt{x}$$