What is the integral of (1+sqrt(x))/(xsqrt(x)) ?

The integral of (1+sqrt(x))/(xsqrt(x)) is -2/(sqrt(x))+ln|x|+C

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integral of (1+sqrt(x))/(xsqrt(x))

\int \frac{1 + x}{x x} d x

- \frac{2}{x} + ln ∣ x ∣ + C

Solution steps

\int \frac{1 + x}{x x} d x

Expand

\frac{1 + x}{x x} : \frac{1}{x x} + \frac{1}{x}

= \int \frac{1}{x x} + \frac{1}{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{1}{x x} d x + \int \frac{1}{x} d x

\int \frac{1}{x x} d x = - \frac{2}{x}

\int \frac{1}{x} d x = ln ∣ x ∣

= - \frac{2}{x} + ln ∣ x ∣

Add a constant to the solution

= - \frac{2}{x} + ln ∣ x ∣ + C

\frac{d y}{d x} + 2 y = 0

\frac{d}{d x} (\frac{2 x sin ( x )}{3 + cos ( x )})

\int_{4}^{1} 2 e^{(x + 3)} d x

\frac{d}{d x} (ln (4) (x))

y^{^{''}} - 2 y^{^{'}} = 8 sin (x) + 2 x e^{x}

What is the integral of (1+sqrt(x))/(xsqrt(x)) ?
The integral of (1+sqrt(x))/(xsqrt(x)) is -2/(sqrt(x))+ln|x|+C