What is the integral of 3/((2-x)^2) ?

The integral of 3/((2-x)^2) is 3/(2-x)+C

integral of 3/((2-x)^2)

integral

\frac{3}{( 2 - x ) ^{2}}

\frac{3}{2 - x} + C

Solution steps

\int \frac{3}{( 2 - x ) ^{2}} d x

Take the constant out:

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

= 3 \cdot \int \frac{1}{( 2 - x ) ^{2}} d x

Apply u-substitution

= 3 \cdot \int - \frac{1}{u ^{2}} d u

Take the constant out:

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

= 3 (- \int \frac{1}{u ^{2}} d u)

Apply the Power Rule

= 3 (- (- \frac{1}{u}))

Substitute back

u = 2 - x

= 3 (- (- \frac{1}{2 - x}))

Simplify

3 (- (- \frac{1}{2 - x})) : \frac{3}{2 - x}

= \frac{3}{2 - x}

Add a constant to the solution

= \frac{3}{2 - x} + C

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