What is the integral of 1/((x-2)^2) ?

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

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integral of 1/((x-2)^2)

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

- \frac{1}{x - 2} + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{u ^{2}} d u

= \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - \frac{1}{u}

Substitute back

u = x - 2

= - \frac{1}{x - 2}

Add a constant to the solution

= - \frac{1}{x - 2} + C

\int 3 x^{2} d x

f (t) = t

2 u

\int \frac{1}{7 x + 5} d x

y^{^{''}} + 9 y = sec (3 t)