A Calc Question

#043 / Math Easy

Calculate the indefinite integral of (x^7)-(x^5)+10

Expand Hint
$$$\int x^n \:dx=\frac{x^{n+1}}{n+1}$$$
Hint 2
This is a calculus problem, and can be written as:
$$$\int (x^7-x^5+10)dx=\int (x^7)dx-\int (x^5)dx+10\int (1)dx$$$
This is a calculus problem, and can be written as:
$$$\int (x^7-x^5+10)dx=\int (x^7)dx-\int (x^5)dx+10\int (1)dx$$$
Applying the power rule to the first section of the integral:
$$$\int x^n \:dx=\frac{x^{n+1}}{n+1}\:with\:n=7\rightarrow \int (x^7)\:dx=\frac{x^{8}}{8}$$$
Applying the power rule to the second section of the integral:
$$$\int x^n \:dx=\frac{x^{n+1}}{n+1}\:with\:n=5\rightarrow \int (x^5)\:dx=\frac{x^{6}}{6}$$$
Applying the constant rule to the third section of the integral:
$$$\int (1)dx=x$$$
Finally,
$$$\int (x^7)dx-\int (x^5)dx+10\int (1)dx$$$
$$$=\frac{x^8}{8}-\frac{x^6}{6}+10x+C$$$
$$$\frac{x^8}{8}-\frac{x^6}{6}+10x+C$$$


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