∫ ( c o s x ) d x {\displaystyle \int (cos{\sqrt {x}})dx} = 2 x ∫ ( c o s u ) d u {\displaystyle 2{\sqrt {x}}\int (cosu)du} = 2 ∫ u ( c o s u ) d u {\displaystyle 2\int {u}(cosu)du} = 2 u ( s i n u ) − 2 ∫ ( s i n u ) d u {\displaystyle {2u}(sinu)-{2}\int (sinu)du} = 2 x ( s i n x ) − ( − 2 c o s u ) {\displaystyle {2}{\sqrt {x}}(sin{\sqrt {x}})-(-2cosu)} = 2 x ( s i n x ) + ( 2 c o s x ) + c {\displaystyle {2}{\sqrt {x}}(sin{\sqrt {x}})+(2cos{\sqrt {x}})+{c}}
u {\displaystyle {u}} = x {\displaystyle {\sqrt {x}}}
d u {\displaystyle {du}} = 1 2 x d x {\displaystyle {\frac {1}{2{\sqrt {x}}}}dx}
2 x d u {\displaystyle 2{\sqrt {x}}{du}} = d x {\displaystyle {dx}}
u {\displaystyle {u}} = u {\displaystyle {u}} , d v {\displaystyle {dv}} = c o s u d u {\displaystyle {cosu}du}
d u {\displaystyle {du}} = d u {\displaystyle {du}} , v {\displaystyle {v}} = s i n u {\displaystyle {sinu}}
