What is the integral from 1 to 2 of (y+5y^7)/(y^3) ?

The integral from 1 to 2 of (y+5y^7)/(y^3) is 63/2

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integral from 1 to 2 of (y+5y^7)/(y^3)

\int_{1}^{2} \frac{y + 5 y ^{7}}{y ^{3}} d y

\frac{63}{2}

Decimal

31.5

Solution steps

\int_{1}^{2} \frac{y + 5 y ^{7}}{y ^{3}} d y

Expand

\frac{y + 5 y ^{7}}{y ^{3}} : \frac{1}{y ^{2}} + 5 y^{4}

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

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

\int_{1}^{2} 5 y^{4} d y = 31

= \frac{1}{2} + 31

Simplify

\frac{1}{2} + 31 : \frac{63}{2}

= \frac{63}{2}

What is the integral from 1 to 2 of (y+5y^7)/(y^3) ?
The integral from 1 to 2 of (y+5y^7)/(y^3) is 63/2