حل ∫ 3+x/2

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

تقدير القيمة

$$\frac{x^{2}}{4}+3x+С$$

خطوات الحل

Integrate the sum term by term.

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

Factor out the constant in each of the terms.

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

Find the integral of 3 using the table of common integrals rule \int a\mathrm{d}x=ax.

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

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

$$3x+\frac{x^{2}}{4}$$

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.

$$3x+\frac{x^{2}}{4}+С$$

تفاضل w.r.t. x

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