What is the integral from 1 to 2 of (x^5+7x^2)/(x^2) ?

The integral from 1 to 2 of (x^5+7x^2)/(x^2) is 43/4

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integral from 1 to 2 of (x^5+7x^2)/(x^2)

\int_{1}^{2} \frac{x ^{5} + 7 x ^{2}}{x ^{2}} d x

\frac{43}{4}

Decimal

10.75

Solution steps

\int_{1}^{2} \frac{x ^{5} + 7 x ^{2}}{x ^{2}} d x

Simplify

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

= \int_{1}^{2} x^{3} + 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_{1}^{2} x^{3} d x + \int_{1}^{2} 7 d x

\int_{1}^{2} x^{3} d x = \frac{15}{4}

\int_{1}^{2} 7 d x = 7

= \frac{15}{4} + 7

Simplify

\frac{15}{4} + 7 : \frac{43}{4}

= \frac{43}{4}

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What is the integral from 1 to 2 of (x^5+7x^2)/(x^2) ?
The integral from 1 to 2 of (x^5+7x^2)/(x^2) is 43/4