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

The integral of sqrt(5)ln(x/5) is sqrt(5)(xln(x/5)-x)+C

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

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

5 (x ln (\frac{x}{5}) - x) + C

Solution steps

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

Take the constant out:

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

= 5 \cdot \int ln (\frac{x}{5}) d x

Apply Integration By Parts

: x ln (\frac{x}{5}) - \int 1 d x

= 5 (x ln (\frac{x}{5}) - \int 1 d x)

\int 1 d x = x

= 5 (x ln (\frac{x}{5}) - x)

Add a constant to the solution

= 5 (x ln (\frac{x}{5}) - x) + C

\int \frac{x - 3}{3 x ^{2} + 6 x + 2} d x

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

\int \frac{5 x - 2}{( x + 2 ) ^{2}} d x

\int x^{2} e^{\frac{x}{3}} d x

What is the integral of sqrt(5)ln(x/5) ?
The integral of sqrt(5)ln(x/5) is sqrt(5)(xln(x/5)-x)+C