Evaluate the following integrals. \int\frac{dx}{x^4-1}

bobbie71G

bobbie71G

Answered question

2021-10-16

Evaluate the following integrals.
dxx41

Answer & Explanation

Nathanael Webber

Nathanael Webber

Skilled2021-10-17Added 117 answers

Evaluate:
dxx41
Simplification:
dxx41=dx(x2+1)(x21)
=dx(x2+1)(x+1)(x1)
Now simplify 1(x2+1)(x+1)(x1) using partial fraction method,
1(x2+1)(x+1)(x1)=Ax+Bx2+1+Cx+1+Dx1
1=(Ax+B)(x+1)(x1)+C(x2+1)(x1)+D(x2+1)(x+1)
Put x=1,1=D(2)(2)D=14
Put x=1,1=C(2)(2)C=14
Put x=0,1=BC+DB=C+D1
B=14+141=⇒B=12
Put x=2,1=(2A+B)(3)(1)+C(5)(1)+D(5)(3)
1=6a+3B+5C+15D
6A=1+32+54154=4+6+5154
6A=0A=0
So

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