please help me to solve:

1) integral 2X X / (X X +1)(X X +1) dx

2) integral dx/( X X*XX+X X +2)

Question

please help me to solve: 1) integral 2X *X / (X *X +1)(X *X +1) dx 2) integral dx/( X *X*X*X+X *X +2)

vikas askiitian expert · Answer

1) 2x 2 /(x 2 +1) 2 dx = [2(x 2 +1) - 2]dx/(x 2 +1) 2 =[2/(x 2 +1) - 2/(x 2 +1) 2 ]dx I = 2tan -1 x - 2dx/(x 2 +1) 2 I - 2tan -1 x = -2dx /(x 2 +1) 2 .........................1 taking RHS put x = tan@ so dx = sec 2 @d@ now RHS = -2d@/sec 2 @ = -2cos 2 @ = -(1+cos2@)d@ =-(@ + sin2@ /2) + c =- [ tan -1 x + sin(2tan -1 x)/2] + c put RHS in eq 1 then I = tan -1 x - sin(2tan -1 x) / 2 + c or I = tan -1 x - x/1+x 2 + c

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please help me to solve: 1) integral 2X X / (X X +1)(X X +1) dx 2) integral dx/( X X*XX+X X +2)

please help me to solve:

1) integral 2X X / (X X +1)(X X +1) dx

2) integral dx/( X X*XX+X X +2)

1 Answers

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