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Question Number 113907 by bemath last updated on 16/Sep/20

$$\int \sqrt{x}\cos \left(\sqrt{x}\right)dx$$

Answered by bobhans last updated on 16/Sep/20

$$K=\int \sqrt{x}\cos \left(\sqrt{x}\right)dx$$$$letx=t^2\Rightarrow dx=2tdt$$$$K=\int 2t^2\mathrm{co}stdt=2t^2\sin t+4t\cos t-4\sin t+c$$$$=2x\sin \left(\sqrt{x}\right)+4\sqrt{x}\cos \left(\sqrt{x}\right)-4\sin \left(\sqrt{x}\right)+c$$$$=(2x-4)\sin \left(\sqrt{x}\right)+4\sqrt{x}\cos \left(\sqrt{x}\right)+c$$

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