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Popular >

integral of 2/5-5/x

Solution

\int \frac{2}{5} - \frac{5}{x} d x

Solution

\frac{2}{5} x - 5 ln ∣ x ∣ + C

Solution steps

\int \frac{2}{5} - \frac{5}{x} 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 \frac{2}{5} d x - \int \frac{5}{x} d x

\int \frac{2}{5} d x = \frac{2}{5} x

\int \frac{5}{x} d x = 5 ln ∣ x ∣

= \frac{2}{5} x - 5 ln ∣ x ∣

Add a constant to the solution

= \frac{2}{5} x - 5 ln ∣ x ∣ + C

Popular Examples

integral of 1/((11-10x-x^2)^2)

\int \frac{1}{( 11 - 10 x - x ^{2} ) ^{2}} d x

derivative of 5/(sqrt(x+3))

\frac{d}{d x} (\frac{5}{x + 3})

limit as x approaches+0 of (1-2x)^{1/2}

x \to + 0 lim ((1 - 2 x)^{\frac{1}{2}})

(sin (x))^{2 x}

integral of (3x+1)/(x^2+4x+3)

\int \frac{3 x + 1}{x ^{2} + 4 x + 3} d x

Frequently Asked Questions (FAQ)

What is the integral of 2/5-5/x ?
The integral of 2/5-5/x is 2/5 x-5ln|x|+C