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

The integral from 3 to 4 of y^3+1/(4y^3) is 50407/1152

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

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

\frac{50407}{1152}

Decimal

43.75607 \dots

Solution steps

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

\int_{3}^{4} y^{3} d y = \frac{175}{4}

\int_{3}^{4} \frac{1}{4 y ^{3}} d y = \frac{7}{1152}

= \frac{175}{4} + \frac{7}{1152}

Simplify

\frac{175}{4} + \frac{7}{1152} : \frac{50407}{1152}

= \frac{50407}{1152}

What is the integral from 3 to 4 of y^3+1/(4y^3) ?
The integral from 3 to 4 of y^3+1/(4y^3) is 50407/1152