Evaluate the indefinite integral of x tanh(x^2) using substitution and hyperbolic identities.

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Integral of x tanh(x^2)

Logarithmic and exponential functions warmup

Find \( \int x \tanh x^2 \, dx \).

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What you need first

Integration by substitution
Derivatives of hyperbolic functions
Integration of rational functions yielding logarithms

What this problem tests

Tests the recognition of the chain rule in reverse (u-substitution) and the integration of the hyperbolic tangent function.

This is a standard integration exercise found in introductory calculus courses, testing the ability to combine u-substitution with knowledge of hyperbolic functions.

Integral of x tanh(x^2)

What you need first

What this problem tests

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