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

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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}

y = x, y = 0, y = \frac{1}{x ^{2}}

x \to 0 lim ((1 - 3 x)^{\frac{7}{x}})

\int \frac{t - 3}{t + 1} d t

\int x \cdot (ln (x))^{2} d x

\frac{d}{d x} (\frac{x + 1}{x ^{2} - y + 1})

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