What is the integral from 1 to 5 of 3+4x^{-4} ?

The integral from 1 to 5 of 3+4x^{-4} is 4996/375

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integral from 1 to 5 of 3+4x^{-4}

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

\frac{4996}{375}

Decimal

13.32266 \dots

Solution steps

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

4 x^{- 4} = \frac{4}{x ^{4}}

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

\int_{1}^{5} 3 d x = 12

\int_{1}^{5} \frac{4}{x ^{4}} d x = \frac{496}{375}

= 12 + \frac{496}{375}

Simplify

12 + \frac{496}{375} : \frac{4996}{375}

= \frac{4996}{375}

What is the integral from 1 to 5 of 3+4x^{-4} ?
The integral from 1 to 5 of 3+4x^{-4} is 4996/375