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1

Solved example of factorization

$\int\left(4x^3+5\right)\left(4x^3-5\right)dx$
2

Solve the product $\left(4x^3+5\right)\left(4x^3-5\right)$

$\int\left(16x^{6}-25\right)dx$
3

The integral of the sum of two or more functions is equal to the sum of their integrals

$\int16x^{6}dx+\int-25dx$
4

The integral of a constant is equal to the constant times the integral's variable

$\int16x^{6}dx-25x$
5

The integral of a constant by a function is equal to the constant multiplied by the integral of the function

$16\int x^{6}dx-25x$
6

Apply the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a constant function

$\frac{16x^{7}}{7}-25x$
7

Take $\frac{16}{7}$ out of the fraction

$\frac{16}{7}x^{7}-25x$
8

As the integral that we are solving is an indefinite integral, when we finish we must add the constant of integration

$\frac{16}{7}x^{7}-25x+C_0$

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