-x2-1x4-3x2-1tan-1 x2-1x dx-

The correct option is D log tan^ 1 ( x+1x )+c ...

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Integration of Piecewise Continuous Functions

∫x2-1x4+3x2+1...

Question

$\int \frac{(x^{2} - 1)}{(x^{4} + 3 x^{2} + 1) {tan}^{- 1} (\frac{x^{2} + 1}{x})} d x$ =

log {sin}^{- 1} (x - \frac{1}{x}) + c

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log {tan}^{- 1} (x - \frac{1}{x}) + c

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log {sin}^{- 1} (x + \frac{1}{x}) + c

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log {tan}^{- 1} (x + \frac{1}{x}) + c

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Solution

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Similar questions

\int \frac{(x^{2} - 1)}{(x^{4} + 3 x^{2} + 1) {tan}^{- 1} (x + \frac{1}{x})} d x

\int \frac{(x^{2} - 1) d x}{(x^{4} + 3 x^{2} + 1) {tan}^{- 1} (x + \frac{1}{x})} = \frac{1}{2} log {tan}^{- 1} (x + \frac{1}{x})

\int \frac{x^{2} - 1}{(x^{4} + 3 x^{2} + 1) {tan}^{- 1} (x + \frac{1}{x})} d x

\int \frac{x^{2} - 2}{(x^{4} + 5 x^{2} + 4) tan (\frac{x^{2} + 2}{x})} d x = log {tan}^{- 1} (x + \frac{2}{x})

\int \frac{x^{2} - 1}{(x^{4} + 3 x^{2} + 1) {tan}^{- 1} (x + \frac{1}{x})} d x

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