∫ 0 π e c o s t ( s i n 2 t ) d t {\displaystyle \int _{0}^{\pi }e^{cost}(sin2t)dt} = ∫ 0 π e c o s t ( 2 s i n t c o s t ) d t {\displaystyle \int _{0}^{\pi }e^{cost}(2sintcost)dt} = − 2 ∫ c o s 0 c o s π e u u d u {\displaystyle {-2}\int _{cos0}^{cos\pi }e^{u}{u}du} = − 2 u e u | c o s 0 c o s π − ( − 2 ) ∫ c o s 0 c o s π e u d u {\displaystyle {-2}{u}e^{u}{\bigg |}_{cos0}^{cos\pi }-(-2)\int _{cos0}^{cos\pi }e^{u}du}
u {\displaystyle {u}} = ( c o s t ) {\displaystyle (cost)}
d u {\displaystyle {du}} = ( − s i n t ) d t {\displaystyle (-sint)dt}
− d u {\displaystyle {-du}} = ( s i n t ) d t {\displaystyle (sint)dt}
