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Question Number 89286 by M±th+et£s last updated on 16/Apr/20
show that  ∫_0 ^1 (((x^2 +1)ln(1+x))/(x^4 −x^2 +1))dx=(π/6)ln(2+(√3))
showthat01(x2+1)ln(1+x)x4x2+1dx=π6ln(2+3)
Answered by TANMAY PANACEA. last updated on 16/Apr/20
∫((1+(1/x^2 ))/(x^2 +(1/x^2 )−1)).ln(1+x)dx  ln(1+x)∫((d(x−(1/x))^ )/((x−(1/x))^2 +1))−∫[(1/(1+x))∫((d(x−(1/x)))/((x−(1/x))^2 +1))dx]dx  ln(1+x).tan^(−1) (x−(1/x))−∫((tan^(−1) (x−(1/x)))/(1+x))dx  wait...
1+1x2x2+1x21.ln(1+x)dxln(1+x)d(x1x)(x1x)2+1[11+xd(x1x)(x1x)2+1dx]dxln(1+x).tan1(x1x)tan1(x1x)1+xdxwait
Commented by M±th+et£s last updated on 16/Apr/20
ok sir
oksir
Answered by M±th+et£s last updated on 16/Apr/20

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