What is the solution for du= 1/(2sqrt(x))dx ?

The solution for du= 1/(2sqrt(x))dx is u(x)=sqrt(x)+c_{1}

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du= 1/(2sqrt(x))dx

d u = \frac{1}{2 x} d x

u (x) = x + c_{1}

Solution steps

d u (x) = \frac{1}{2 x} d x

Let

u (x)

be the dependent variable. Divide by

d x

\frac{d u ( x )}{d x} = \frac{1}{2 x}

Substitute

\frac{d u ( x )}{d x}

with

u^{'} (x)

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

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

u (x) = \int \frac{1}{2 x} d x

\int \frac{1}{2 x} d x = x + c_{1}

u (x) = x + c_{1}

What is the solution for du= 1/(2sqrt(x))dx ?
The solution for du= 1/(2sqrt(x))dx is u(x)=sqrt(x)+c_{1}