What is the integral from 1 to 2 of (y+4y^6)/(y^3) ?

The integral from 1 to 2 of (y+4y^6)/(y^3) is 31/2

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integral from 1 to 2 of (y+4y^6)/(y^3)

\int_{1}^{2} \frac{y + 4 y ^{6}}{y ^{3}} d y

\frac{31}{2}

Decimal Notation

15.5

Solution steps

\int_{1}^{2} \frac{y + 4 y ^{6}}{y ^{3}} d y

Simplify

\frac{y + 4 y ^{6}}{y ^{3}} : \frac{1 + 4 y ^{5}}{y ^{2}}

= \int_{1}^{2} \frac{1 + 4 y ^{5}}{y ^{2}} d y

Expand

\frac{1 + 4 y ^{5}}{y ^{2}} : \frac{1}{y ^{2}} + 4 y^{3}

= \int_{1}^{2} \frac{1}{y ^{2}} + 4 y^{3} d y

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{1}{y ^{2}} d y + \int_{1}^{2} 4 y^{3} d y

\int_{1}^{2} \frac{1}{y ^{2}} d y = \frac{1}{2}

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

= \frac{1}{2} + 15

Simplify

\frac{1}{2} + 15 : \frac{31}{2}

= \frac{31}{2}

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What is the integral from 1 to 2 of (y+4y^6)/(y^3) ?
The integral from 1 to 2 of (y+4y^6)/(y^3) is 31/2