What is the integral from 1 to 3 of (x^5+1/(4x^5)) ?

The integral from 1 to 3 of (x^5+1/(4x^5)) is 9833/81

integral from 1 to 3 of (x^5+1/(4x^5))

\int_{1}^{3} (x^{5} + \frac{1}{4 x ^{5}}) d x

\frac{9833}{81}

Decimal

121.39506 \dots

Solution steps

\int_{1}^{3} x^{5} + \frac{1}{4 x ^{5}} 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}^{3} x^{5} d x + \int_{1}^{3} \frac{1}{4 x ^{5}} d x

\int_{1}^{3} x^{5} d x = \frac{364}{3}

\int_{1}^{3} \frac{1}{4 x ^{5}} d x = \frac{5}{81}

= \frac{364}{3} + \frac{5}{81}

Simplify

\frac{364}{3} + \frac{5}{81} : \frac{9833}{81}

= \frac{9833}{81}

t an g e n t f (x) = \frac{3}{x}, (- 5, - \frac{3}{5})

n = 0 \sum \infty sin (\frac{1}{n})

\int x^{2} 5 x + 8 d x

d er i v a t i v e 6 (x - 3)^{\frac{2}{3}}

\int_{1}^{9} \frac{1}{x - 5} d x

What is the integral from 1 to 3 of (x^5+1/(4x^5)) ?
The integral from 1 to 3 of (x^5+1/(4x^5)) is 9833/81