Step-by-step Solution

Integral of $\frac{1}{x^2-36}$ with respect to x

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Step-by-step explanation

Problem to solve:

$\int\frac{1}{x^2-36}dx$

Learn how to solve integrals by partial fraction expansion problems step by step online.

$\int\frac{1}{\left(x+6\right)\left(x-6\right)}dx$

Unlock this full step-by-step solution!

Learn how to solve integrals by partial fraction expansion problems step by step online. Integral of 1/(x^2-36) with respect to x. Factor the difference of squares x^2-36 as the product of two conjugated binomials. Rewrite the fraction \frac{1}{\left(x+6\right)\left(x-6\right)} in 2 simpler fractions using partial fraction decomposition. Find the values of the unknown coefficients. The first step is to multiply both sides of the equation by \left(x+6\right)\left(x-6\right). Multiplying polynomials.

Final Answer

$-\frac{1}{12}\ln\left|x+6\right|+\frac{1}{12}\ln\left|x-6\right|+C_0$

Problem Analysis