What is the integral of 1/((x-7)^2) ?

The integral of 1/((x-7)^2) is -1/(x-7)+C

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integral of 1/((x-7)^2)

\int \frac{1}{( x - 7 ) ^{2}} d x

- \frac{1}{x - 7} + C

Solution steps

\int \frac{1}{( x - 7 ) ^{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 - 7

= - \frac{1}{x - 7}

Add a constant to the solution

= - \frac{1}{x - 7} + C

y^{^{''}} - 5 y^{^{'}} - 6 y = 12 e^{2 t}

x \to 0 lim (\frac{1}{( x - 1 ) ^{2}} + 2)

\frac{d y}{d x} + 10 y = 11

\frac{d}{d x} (x^{2} - 4 x + 10)