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,

$$$\int (x^7)dx-\int (x^5)dx+10\int (1)dx$$$

$$$=\frac{x^8}{8}-\frac{x^6}{6}+10x+C$$$

$$$\frac{x^8}{8}-\frac{x^6}{6}+10x+C$$$

Time Analysis

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