What is the integral from 1 to 2 of (v^6+4v^8)/(v^5) ?

The integral from 1 to 2 of (v^6+4v^8)/(v^5) is 33/2

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integral from 1 to 2 of (v^6+4v^8)/(v^5)

\int_{1}^{2} \frac{v ^{6} + 4 v ^{8}}{v ^{5}} d v

\frac{33}{2}

Decimal

16.5

Solution steps

\int_{1}^{2} \frac{v ^{6} + 4 v ^{8}}{v ^{5}} d v

Expand

\frac{v ^{6} + 4 v ^{8}}{v ^{5}} : \frac{v ^{6}}{v ^{5}} + \frac{4 v ^{8}}{v ^{5}}

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} \frac{v ^{6}}{v ^{5}} d v + \int_{1}^{2} \frac{4 v ^{8}}{v ^{5}} d v

\int_{1}^{2} \frac{v ^{6}}{v ^{5}} d v = \frac{3}{2}

\int_{1}^{2} \frac{4 v ^{8}}{v ^{5}} d v = 15

= \frac{3}{2} + 15

Simplify

\frac{3}{2} + 15 : \frac{33}{2}

= \frac{33}{2}

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What is the integral from 1 to 2 of (v^6+4v^8)/(v^5) ?
The integral from 1 to 2 of (v^6+4v^8)/(v^5) is 33/2