What is the integral of (8000ln(x+25))/((x+25)^2) ?

The integral of (8000ln(x+25))/((x+25)^2) is 8000(-(ln(x+25))/(x+25)-1/(x+25))+C

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integral of (8000ln(x+25))/((x+25)^2)

\int \frac{8000 ln ( x + 25 )}{( x + 25 ) ^{2}} d x

8000 (- \frac{ln ( x + 25 )}{x + 25} - \frac{1}{x + 25}) + C

Solution steps

\int \frac{8000 ln ( x + 25 )}{( x + 25 ) ^{2}} d x

Take the constant out:

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

= 8000 \cdot \int \frac{ln ( x + 25 )}{( x + 25 ) ^{2}} d x

Apply Integration By Parts

: - \frac{ln ( x + 25 )}{x + 25} - \int - \frac{1}{( x + 25 ) ^{2}} d x

= 8000 (- \frac{ln ( x + 25 )}{x + 25} - \int - \frac{1}{( x + 25 ) ^{2}} d x)

\int - \frac{1}{( x + 25 ) ^{2}} d x = \frac{1}{x + 25}

= 8000 (- \frac{ln ( x + 25 )}{x + 25} - \frac{1}{x + 25})

Add a constant to the solution

= 8000 (- \frac{ln ( x + 25 )}{x + 25} - \frac{1}{x + 25}) + C

\frac{\partial}{\partial y} (e^{- x yz})

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

(2 + x) \cdot e^{x}

2 y y^{^{'}} + 2 = y^{2} + 2 x, y (0) = 9

\int - 5 d x

What is the integral of (8000ln(x+25))/((x+25)^2) ?
The integral of (8000ln(x+25))/((x+25)^2) is 8000(-(ln(x+25))/(x+25)-1/(x+25))+C