7.1 Integration By Parts/36

$\int _{0}^{\pi }e^{cost}(sin2t)dt$ = $\int _{0}^{\pi }e^{cost}(2sintcost)dt$ = ${-2}\int _{cos0}^{cos\pi }e^{u}{u}du$ = ${-2}{u}e^{u}{\bigg |}_{cos0}^{cos\pi }-(-2)\int _{cos0}^{cos\pi }e^{u}du$

${u}$ = $(cost)$

${du}$ = $(-sint)dt$

${-du}$ = $(sint)dt$

${u}$ = ${u}$ ${dv}$ = $e^{u}du$

${du}$ = ${du}$ ${v}$ = $e^{u}$