Solve ∫ 5x^2*6x^2 wrt x

$$\int{ 5 { x }^{ 2 } \times 6 { x }^{ 2 } }d x$$

Evaluate

$$6x^{5}+С$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\int 5x^{4}\times 6\mathrm{d}x$$

Multiply 5 and 6 to get 30.

$$\int 30x^{4}\mathrm{d}x$$

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

$$30\int x^{4}\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{4}\mathrm{d}x with \frac{x^{5}}{5}. Multiply 30 times \frac{x^{5}}{5}.

$$6x^{5}$$

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.

$$6x^{5}+С$$

Differentiate w.r.t. x

$$30x^{4}$$