How do I find the integral ∫1(w−4)(w+1)dw ?
1 Answer
Jul 28, 2014
=15ln(w−4w+1)+c , wherec is a constant
Explanation :
This type of question usually solve by using Partial Fractions,
1(w−4)(w+1) , it can be written as
1(w−4)(w+1)=Aw−4+Bw+1
multiplying by
1=A(w+1)+B(w−4)
1=(A+B)w+(A−4B)
Now comparing coefficient of
A+B=0 ⇒ A=−B ...........(i)
A−4B=1 ..............(ii)
Substituting value of
−5B=1 ⇒ B=−15
from
Now,
1(w−4)(w+1)=15(w−4)−15(w+1)
Integrating both side with respect to
∫1(w−4)(w+1)dw=∫15(w−4)dw−∫15(w+1)dw
=15(ln(w−4)−ln(w+1))+c , wherec is a constant
=15ln(w−4w+1)+c , wherec is a constant