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" (iii) "tan^(-1)((3x-x^(3))/(1-3x^(2)))...

" (iii) "tan^(-1)((3x-x^(3))/(1-3x^(2)))

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int tan^(-1)((3x-x^(3))/(1-3x^(2)))dx

int tan^(-1)((3x-x^(3))/(1-3x^(2)))dx

Answer the equation: int tan^(-1)((3x-x^(3))/(1-3x^(2)))dx

If f(x)=tan^(-1)((3x-x^(3))/(1-3x^(2))) then (d)/(dx)(f(x)) is equal to

Evaluate the integerals. int tan ^(-1)((3x -x^(3))/(1-3x^(2)))dx on I sub R \\ {-(1)/(sqrt3), (1)/(sqrt3)}.

Define: tan^(-1)((3x-x^(3))/(1-3x^(2))) in terms of tan^(-1)x

Define: tan^(-1)((3x-x^(3))/(1-3x^(2))) in terms of tan^(-1)x

Prove that 3 tan^(-1) x= {(tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " -(1)/(sqrt3) lt x lt (1)/(sqrt3)),(pi + tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " x gt (1)/(sqrt3)),(-pi + tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " x lt - (1)/(sqrt3)):}

Prove that 3 tan^(-1) x= {(tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " -(1)/(sqrt3) lt x lt (1)/(sqrt3)),(pi + tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " x gt (1)/(sqrt3)),(-pi + tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " x lt - (1)/(sqrt3)):}