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Evaluate the integral ∫_ ^ (2x+1)cos(x/2)x. (a) 4(2x+1)sin(x/2)+2cos(x/2)+C …

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Wize University Calculus 1 Textbook > Integration Techniques

Integration by Parts

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Evaluate the integral ∫(2x+1)cos⁡(x/2)  ⁣dx\displaystyle\int_{ }^{ }(2x+1)\cos(x/2)\de{x}.
(a) 4(2x+1)sin⁡(x/2)+2cos⁡(x/2)+C4(2x+1)\sin(x/2)+2\cos(x/2)+C (b) 4(2x+1)sin⁡(x/2)+8cos⁡(x/2)+C4(2x+1)\sin(x/2)+8\cos(x/2)+C
(c) 2(2x+1)sin⁡(x/2)+2cos⁡(x/2)+C2(2x+1)\sin(x/2)+2\cos(x/2)+C (d) 2(2x+1)sin⁡(x/2)+8cos⁡(x/2)+C2(2x+1)\sin(x/2)+8\cos(x/2)+C
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