Question

determine the following indefinite integral. check your work by differentiation.
int (2x^{5}-5x^{14})dx
int (2x^{5}-5x^{14})dx=square

Explanation:

Step1: Apply sum - difference rule of integration

$\int(2x^{5}-5x^{14})dx=\int 2x^{5}dx-\int 5x^{14}dx$

Step2: Use constant - multiple rule of integration

$2\int x^{5}dx - 5\int x^{14}dx$

Step3: Apply power rule of integration $\int x^{n}dx=\frac{x^{n + 1}}{n+1}+C$ ($n

eq - 1$)
$2\times\frac{x^{5 + 1}}{5+1}-5\times\frac{x^{14+1}}{14 + 1}+C$
$=\frac{2x^{6}}{6}-\frac{5x^{15}}{15}+C$

Step4: Simplify the expression

$=\frac{1}{3}x^{6}-\frac{1}{3}x^{15}+C$

Answer:

$\frac{1}{3}x^{6}-\frac{1}{3}x^{15}+C$