What is the integral from 2 to 4 of (5/x-(10)/(x^2)) ?

The integral from 2 to 4 of (5/x-(10)/(x^2)) is 5ln(2)-5/2

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integral from 2 to 4 of (5/x-(10)/(x^2))

\int_{2}^{4} (\frac{5}{x} - \frac{10}{x ^{2}}) d x

5 ln (2) - \frac{5}{2}

Decimal

0.96573 \dots

Solution steps

\int_{2}^{4} \frac{5}{x} - \frac{10}{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_{2}^{4} \frac{5}{x} d x - \int_{2}^{4} \frac{10}{x ^{2}} d x

\int_{2}^{4} \frac{5}{x} d x = 5 ln (2)

\int_{2}^{4} \frac{10}{x ^{2}} d x = \frac{5}{2}

= 5 ln (2) - \frac{5}{2}

\int \frac{( e ^{x} )}{1 + e ^{2 x}} d x

y^{^{'}} + a \cdot y = b

\frac{d}{d x} (2 x + 2 (cos (x) + 1) sin (x))

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f (x) = \frac{1 + 4 x}{9 - 6 x}

What is the integral from 2 to 4 of (5/x-(10)/(x^2)) ?
The integral from 2 to 4 of (5/x-(10)/(x^2)) is 5ln(2)-5/2