What is the integral of (5000ln(x+20))/((x+20)^2) ?

The integral of (5000ln(x+20))/((x+20)^2) is 5000(-(ln(x+20))/(x+20)-1/(x+20))+C

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integral of (5000ln(x+20))/((x+20)^2)

\int \frac{5000 ln ( x + 20 )}{( x + 20 ) ^{2}} d x

5000 (- \frac{ln ( x + 20 )}{x + 20} - \frac{1}{x + 20}) + C

Solution steps

\int \frac{5000 ln ( x + 20 )}{( x + 20 ) ^{2}} d x

Take the constant out:

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

= 5000 \cdot \int \frac{ln ( x + 20 )}{( x + 20 ) ^{2}} d x

Apply Integration By Parts

: - \frac{ln ( x + 20 )}{x + 20} - \int - \frac{1}{( x + 20 ) ^{2}} d x

= 5000 (- \frac{ln ( x + 20 )}{x + 20} - \int - \frac{1}{( x + 20 ) ^{2}} d x)

\int - \frac{1}{( x + 20 ) ^{2}} d x = \frac{1}{x + 20}

= 5000 (- \frac{ln ( x + 20 )}{x + 20} - \frac{1}{x + 20})

Add a constant to the solution

= 5000 (- \frac{ln ( x + 20 )}{x + 20} - \frac{1}{x + 20}) + C

\frac{d}{d x} (- 5 e^{3 x})

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

\frac{d}{d x} (\frac{e ^{5 x}}{x ^{15}})

\frac{d}{d x} (b (x + a)^{3} + c)

What is the integral of (5000ln(x+20))/((x+20)^2) ?
The integral of (5000ln(x+20))/((x+20)^2) is 5000(-(ln(x+20))/(x+20)-1/(x+20))+C