Integration with partial fractions | AP Calculus BC | Khan Academy

Finding the integral of a rational function using linear partial fraction decomposition.

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[omkarsawant]

Maths is beautiful when we have teachers like you👍👍

[Salamanca-joro]

I solved it the same way !! Great ! Now i can move forward to the next topic

[michalchik]

There's a much easier way to do this. Since the constants A&B have to be true for all values of x. And since the denominators are the same on both sides, just look at the numerators and set them as an equation.

X - 5= a(x -1) + b(2x-3)

First set x = 1, turning x -1 into 0, so the equation becomes

1-5=b(2*1-3)
Simplifying b equals 4. You can do the same thing, by picking x equals 3/2, cancelling out the b part of the equation, and solving for a

[edwardrk]

thankyou bro, I understand partial fraction now !!

[rafi_xoss]

I loved it, helped me a lot. Take love from your own Bangladesh.

[hotnika]

I solved by taking out the 1/2 from 1/2x-3 and solved -7/2*ln|x-3/2| out but seems that it is different with the result of -7/2*ln|2x-3| when substituting numbers into them, am I wrong?