Integrals

#040 / Math Easy

Calculate the indefinite integral of (x^4)-(x^2)+2

Expand Hint

$$$\int x^n \:dx=\frac{x^{n+1}}{n+1}$$$

Hint 2

This is a calculus problem, and can be written as:

$$$\int (x^4-x^2+2)dx=\int (x^4)dx-\int (x^2)dx+2\int (1)dx$$$

This is a calculus problem, and can be written as:

$$$\int (x^4-x^2+2)dx=\int (x^4)dx-\int (x^2)dx+2\int (1)dx$$$

Applying the power rule to the first section of the integral:

$$$\int x^n \:dx=\frac{x^{n+1}}{n+1}\:with\:n=4\rightarrow \int (x^4)\:dx=\frac{x^{5}}{5}$$$

Applying the power rule to the second section of the integral:

$$$\int x^n \:dx=\frac{x^{n+1}}{n+1}\:with\:n=2\rightarrow \int (x^2)\:dx=\frac{x^{3}}{3}$$$

Applying the constant rule to the third section of the integral:

$$$\int (1)dx=x$$$

Finally,

$$$\int (x^4)dx-\int (x^2)dx+2\int (1)dx$$$

$$$=\frac{x^5}{5}-\frac{x^3}{3}+2x+C$$$

$$$\frac{x^5}{5}-\frac{x^3}{3}+2x+C$$$

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