Verify the Integration Formula$$\int \tanh ^ { - 1 } x d x = x \tanh ^ { - 1 } x + \frac { 1 } { 2 } \ln \left( 1 - x ^ { 2 } \right) + C$$

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The Answer of Verify the Integration Formula$$\int \tanh ^ { - 1 } x d x = x \tanh ^ { - 1 } x + \frac { 1 } { 2 } \ln \left( 1 - x ^ { 2 } \right) + C$$

Verify the Integration Formula $\int \tanh ^ { - 1 } x d x = x \tanh ^ { - 1 } x + \frac { 1 } { 2 } \ln \left( 1 - x ^ { 2 } \right) + C$

Definitions:

Verify the Integration Formula ∫tanh⁡−1xdx=xtanh⁡−1x+12ln⁡(1−x2)+C\int \tanh ^ { - 1 } x d x = x \tanh ^ { - 1 } x + \frac { 1 } { 2 } \ln \left( 1 - x ^ { 2 } \right) + C∫tanh−1xdx=xtanh−1x+21​ln(1−x2)+C

Definitions:

Verify the Integration Formula $\int \tanh ^ { - 1 } x d x = x \tanh ^ { - 1 } x + \frac { 1 } { 2 } \ln \left( 1 - x ^ { 2 } \right) + C$