What is the integral of (x')/(sqrt(x)) ?

The integral of (x')/(sqrt(x)) is sqrt(x)x'+1/(2sqrt(x))+C

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integral of (x')/(sqrt(x))

\int \frac{x ^{'}}{x} d x

x x' + \frac{1}{2 x} + C

Solution steps

\int \frac{x ^{'}}{x} d x

Apply Integration By Parts

: x x^{'} - \int \frac{1}{4 x ^{\frac{3}{2}}} d x

= x x^{^{'}} - \int \frac{1}{4 x ^{\frac{3}{2}}} d x

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

= x x^{^{'}} - (- \frac{1}{2 x})

Simplify

= x x^{^{'}} + \frac{1}{2 x}

Add a constant to the solution

= x x^{^{'}} + \frac{1}{2 x} + C

x \to - \infty lim (- 4)

\int e^{u} d u

\frac{100}{s ^{3} ( s - 2 )}

x \to - 5 lim (217)

n = 1 \sum \infty 3^{n} \frac{1}{n !}

What is the integral of (x')/(sqrt(x)) ?
The integral of (x')/(sqrt(x)) is sqrt(x)x'+1/(2sqrt(x))+C