# How do you integrate #(2x)/((x-1)(x+1))# using partial fractions?

The given expression can be written as partial sum of fractions:

Now let's integrate :

By signing up, you agree to our Terms of Service and Privacy Policy

To integrate ( \frac{2x}{(x-1)(x+1)} ) using partial fractions, first, we express the fraction as a sum of simpler fractions:

[ \frac{2x}{(x-1)(x+1)} = \frac{A}{x-1} + \frac{B}{x+1} ]

We then solve for ( A ) and ( B ) by equating numerators:

[ 2x = A(x+1) + B(x-1) ]

Now, we can solve for ( A ) and ( B ) by substituting suitable values for ( x ). For instance, setting ( x = 1 ) gives:

[ 2 = 2A ]

And setting ( x = -1 ) gives:

[ -2 = -2B ]

Thus, ( A = 1 ) and ( B = -1 ).

Now, we can rewrite the original fraction as:

[ \frac{1}{x-1} - \frac{1}{x+1} ]

Integrating each term separately gives:

[ \int \frac{1}{x-1} , dx - \int \frac{1}{x+1} , dx ]

[ = \ln|x-1| - \ln|x+1| + C ]

Therefore, the integral of ( \frac{2x}{(x-1)(x+1)} ) using partial fractions is ( \ln|x-1| - \ln|x+1| + C ), where ( C ) is the constant of integration.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find the sum of the infinite series #Sigma(1/10)^k# from k=1 to #oo#?
- What is #int ln4x^2dx#?
- What is the antiderivative of #e^(-3x)#?
- How do you use sigma notation to write the sum for #1/(1*3)+1/(2*4)+1/(3*5)+...+1/(10*12)#?
- How do you integrate #(5x)/(2x^2+11x+12)# using partial fractions?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7