What is the integral of (x^4-5x^3+7x)/x ?

The integral of (x^4-5x^3+7x)/x is (x^4)/4-(5x^3)/3+7x+C

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integral of (x^4-5x^3+7x)/x

\int \frac{x ^{4} - 5 x ^{3} + 7 x}{x} d x

\frac{x ^{4}}{4} - \frac{5 x ^{3}}{3} + 7 x + C

Solution steps

\int \frac{x ^{4} - 5 x ^{3} + 7 x}{x} d x

Simplify

\frac{x ^{4} - 5 x ^{3} + 7 x}{x} : x^{3} - 5 x^{2} + 7

= \int x^{3} - 5 x^{2} + 7 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x^{3} d x - \int 5 x^{2} d x + \int 7 d x

\int x^{3} d x = \frac{x ^{4}}{4}

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

\int 7 d x = 7 x

= \frac{x ^{4}}{4} - \frac{5 x ^{3}}{3} + 7 x

Add a constant to the solution

= \frac{x ^{4}}{4} - \frac{5 x ^{3}}{3} + 7 x + C

x \to 6 lim (\frac{g ( x )}{f ( x )})

\int \frac{cos ^{2} ( x )}{sin ^{2} ( x )} d x

\frac{d}{d x} (7 x^{2} - 5 x + 3)

\frac{( 3 e ^{3 x} )}{3}

\int \frac{1}{x ^{2} - 5 x + 4} d x

What is the integral of (x^4-5x^3+7x)/x ?
The integral of (x^4-5x^3+7x)/x is (x^4)/4-(5x^3)/3+7x+C