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

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

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integral of 1/((a+x)^2)

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

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

Solution steps

\int \frac{1}{( a + x ) ^{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 = a + x

= - \frac{1}{a + x}

Add a constant to the solution

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

x^{4} - 3 x^{2} + 1, 1

y = e^{x} (x + x x)

x \to - 2 lim (4 x^{2} - 3)

n = - 4 \sum \infty (- \frac{4}{5})^{n}

y = \frac{1}{3} x^{3} - 2 x + 2, (- 3, - 1)