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\int 6x^{2}\mathrm{d}x+\int 8x\mathrm{d}x+\int 3\mathrm{d}x
Integrate the sum term by term.
6\int x^{2}\mathrm{d}x+8\int x\mathrm{d}x+\int 3\mathrm{d}x
Factor out the constant in each of the terms.
2x^{3}+8\int x\mathrm{d}x+\int 3\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}. اضرب 6 في \frac{x^{3}}{3}.
2x^{3}+4x^{2}+\int 3\mathrm{d}x
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 8 في \frac{x^{2}}{2}.
2x^{3}+4x^{2}+3x
Find the integral of 3 using the table of common integrals rule \int a\mathrm{d}x=ax.
2x^{3}+4x^{2}+3x+С
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.