Solve ∫ 3(u^2)^2/udu

$$\int \frac { 3 ( u ^ { 2 } ) ^ { 2 } } { u } d u$$

Evaluate

$$\frac{3u^{4}}{4}+С$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\int \frac{3u^{4}}{u}\mathrm{d}u$$

Cancel out u in both numerator and denominator.

$$\int 3u^{3}\mathrm{d}u$$

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

$$3\int u^{3}\mathrm{d}u$$

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

$$\frac{3u^{4}}{4}$$

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

$$\frac{3u^{4}}{4}+С$$

Differentiate w.r.t. u

$$3u^{3}$$