What is the integral from 1 to 4 of 2x+1/(x^2) ?

The integral from 1 to 4 of 2x+1/(x^2) is 63/4

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integral from 1 to 4 of 2x+1/(x^2)

\int_{1}^{4} 2 x + \frac{1}{x ^{2}} d x

\frac{63}{4}

Decimal

15.75

Solution steps

\int_{1}^{4} 2 x + \frac{1}{x ^{2}} 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}^{4} 2 x d x + \int_{1}^{4} \frac{1}{x ^{2}} d x

\int_{1}^{4} 2 x d x = 15

\int_{1}^{4} \frac{1}{x ^{2}} d x = \frac{3}{4}

= 15 + \frac{3}{4}

Simplify

15 + \frac{3}{4} : \frac{63}{4}

= \frac{63}{4}

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What is the integral from 1 to 4 of 2x+1/(x^2) ?
The integral from 1 to 4 of 2x+1/(x^2) is 63/4