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

The integral of ((sqrt(5x))/5+5/(sqrt(5x))) is 2/(3sqrt(5))x^{3/2}+2sqrt(5)sqrt(x)+C

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integral of ((sqrt(5x))/5+5/(sqrt(5x)))

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

\frac{2}{3 5} x^{\frac{3}{2}} + 25 x + C

Solution steps

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

\int \frac{5 x}{5} d x = \frac{2}{3 5} x^{\frac{3}{2}}

\int \frac{5}{5 x} d x = 25 x

= \frac{2}{3 5} x^{\frac{3}{2}} + 25 x

Add a constant to the solution

= \frac{2}{3 5} x^{\frac{3}{2}} + 25 x + C

y^{^{''}} + y^{^{'}} - 12 y = 3 e^{2 x}

y^{^{''}} + 6 y^{^{'}} + 8 y = - 6 t e^{4 t}

\int_{1}^{2} \frac{1}{x ( x - 5 )} d x

\int \frac{1}{x 2 + 9 x ^{2}} d x

f (x) = \frac{2 x + 5}{x}

What is the integral of ((sqrt(5x))/5+5/(sqrt(5x))) ?
The integral of ((sqrt(5x))/5+5/(sqrt(5x))) is 2/(3sqrt(5))x^{3/2}+2sqrt(5)sqrt(x)+C