Evaluate
x^{3}+x^{2}+С
Differentiate w.r.t. x
x\left(3x+2\right)
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\int 2x\mathrm{d}x+\int 3x^{2}\mathrm{d}x
Integrate the sum term by term.
2\int x\mathrm{d}x+3\int x^{2}\mathrm{d}x
Factor out the constant in each of the terms.
x^{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\mathrm{d}x with \frac{x^{2}}{2}. Multiply 2 times \frac{x^{2}}{2}.
x^{2}+x^{3}
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}. Multiply 3 times \frac{x^{3}}{3}.
x^{2}+x^{3}+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.
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