# How do you integrate #x/(x+10)#?

A simple substitution will do.

Rewrite and simplify:

Integrate:

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To integrate ( \frac{x}{x+10} ), you can use a technique called partial fraction decomposition. After decomposition, integrate each term separately.

The decomposition of ( \frac{x}{x+10} ) is:

[ \frac{x}{x+10} = \frac{A}{x+10} + \frac{B}{x} ]

To solve for ( A ) and ( B ), multiply both sides by the common denominator ( x(x+10) ), then equate the numerators.

Once you have found ( A ) and ( B ), integrate each term separately:

[ \int \frac{x}{x+10} , dx = A \ln|x+10| + B \ln|x| + C ]

Where ( C ) is the constant of integration.

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