What is the integral of [(sqrt(x)+3)/(5sqrt(x))] ?

The integral of [(sqrt(x)+3)/(5sqrt(x))] is 1/5 (sqrt(x)+3)^2+C

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integral of [(sqrt(x)+3)/(5sqrt(x))]

\int [\frac{x + 3}{5 x}] d x

\frac{1}{5} (x + 3)^{2} + C

Solution steps

\int \frac{x + 3}{5 x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{5} \cdot \int \frac{x + 3}{x} d x

Apply u-substitution

: \int 2 u d u

= \frac{1}{5} \cdot \int 2 u d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{5} \cdot 2 \cdot \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= \frac{1}{5} \cdot 2 \cdot \frac{u ^{2}}{2}

Substitute back

u = x + 3

= \frac{1}{5} \cdot 2 \cdot \frac{( x + 3 ) ^{2}}{2}

Simplify

\frac{1}{5} \cdot 2 \cdot \frac{( x + 3 ) ^{2}}{2} : \frac{1}{5} (x + 3)^{2}

= \frac{1}{5} (x + 3)^{2}

Add a constant to the solution

= \frac{1}{5} (x + 3)^{2} + C

\int \frac{( e ^{x} )}{( e ^{x} - 1 ) ( e ^{x} + 3 )} d x

y^{^{'}} = (π \cdot x + y + π^{2})^{2}

\int ln (3 x^{2}) d x

\int sin^{4} (b)

12 x e^{x}

What is the integral of [(sqrt(x)+3)/(5sqrt(x))] ?
The integral of [(sqrt(x)+3)/(5sqrt(x))] is 1/5 (sqrt(x)+3)^2+C