Solve ∫ 13/12x^3 wrt x=

$$\int \frac { 13 } { 12 } x ^ { 3 } d x =$$

Evaluate

$$\frac{13x^{4}}{48}+С$$

Solution Steps

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

$$\frac{13\int x^{3}\mathrm{d}x}{12}$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{3}\mathrm{d}x with \frac{x^{4}}{4}.

$$\frac{13x^{4}}{48}$$

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.

$$\frac{13x^{4}}{48}+С$$

Differentiate w.r.t. x

$$\frac{13x^{3}}{12}$$