Evaluate the expression .

MATHEMATICS · Multi-part · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Evaluate the expression ∫x (x2+5)4 cos⁡[(x2+5)5] dx\displaystyle \int x\,(x^{2}+5)^{4}\,\cos\bigl[(x^{2}+5)^{5}\bigr]\,dx. (i) Obtain the antiderivative in its simplest closed form. (ii) Confirm the correctness of your result by differentiating your answer and showing that it reproduces the given integrand.

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