Solve ∫ 2ndn

$$\int 2 n d n$$

Evaluate

$$n^{2}+С$$

Solution Steps

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

$$2\int n\mathrm{d}n$$

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

$$n^{2}$$

If F\left(n\right) is an antiderivative of f\left(n\right), then the set of all antiderivatives of f\left(n\right) is given by F\left(n\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$n^{2}+С$$

Differentiate w.r.t. n

$$2n$$