Question

determine the following indefinite integral
int\frac{4x^{7}+6x^{5}}{x^{4}}dx
int\frac{4x^{7}+6x^{5}}{x^{4}}dx=square

Explanation:

Step1: Simplify the integrand

$\int\frac{4x^{7}+6x^{5}}{x^{4}}dx=\int(4x^{7 - 4}+6x^{5 - 4})dx=\int(4x^{3}+6x)dx$

Step2: Integrate term - by - term

Using the power rule for integration $\int x^{n}dx=\frac{x^{n + 1}}{n+1}+C$ ($n
eq - 1$), we have $\int(4x^{3}+6x)dx=4\times\frac{x^{3 + 1}}{3+1}+6\times\frac{x^{1+1}}{1 + 1}+C$
$=4\times\frac{x^{4}}{4}+6\times\frac{x^{2}}{2}+C$

Step3: Simplify the result

$x^{4}+3x^{2}+C$

Answer:

$x^{4}+3x^{2}+C$