So what we wanna do is multiply this first rational expression by x-1 in the numeratorĪnd the denominator. How do we solve for A and B? Well, let's add them as if we're just adding two fractions with unlike denominators. This is more precalculus now, or algebra. So our denominators here are first degree, so our numerator's gonna be Gonna be one degree less than your denominator. But the general principle here is that your numerator is If this the first time you're ever seeing partialįraction decomposition, look that up on Khan Academy.
As you might have learned before, and I encourage you, Second rational expression is x-1, and I don't have to Of two rational expressions, where the denominator of theįirst rational expression is 2x-3, and the denominator of the So what we're gonna try to do with partial fractionĭecomposition is say, can we express x-5 over (2x-3)(x-1), can we express it as a sum And a good hint there is the fact that this denominator here is factorable into these two expressions. Up this rational expression into the sum of two rational expressions. Partial fraction decomposition, which might invoke some memoriesįrom a precalculus class or maybe from an algebra 2 class, but it's a technique to break So what do we do? And my hint to you would be Here the derivative or a constant multiple of theĭerivative of the denominator? In which case, u-substitution might apply, but it's not the case here. This, might try to say, all right, is the numerator Asked to find the value of this indefinite integral.
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