(a) Use the substitution $u = \tan^{-1} x$ to find the integral \(\int \frac{1}{1 + x^2} \sin^3(\tan^{-1} x) \, dx.\) (b) Use integration by substitution and then a hyperbolic half-variable identity to find the integral \(\int 2x \cosh^2(x^2) \, dx.\)
Added by Oscar W.
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This means that x = tan(u) and dx = sec^2(u) du. Show more…
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