\large x\cdot\cos{\:x}-{{{{{{{\displaystyle\int\sin{\:x}{\:d}x=x\cdot\cos{\:x}-\left(-\cos\:{x}+C\right)=x\cdot\cos{\:x}+\cos{\:x}+C}}}}}}}Unchecked
\large x\cdot\sin{\:x}+{{{{{{{\displaystyle\int\cos{\:x}{\:d}x=x\cdot\sin{\:x}-\left(-\sin\:{x}+C\right)=x\cdot\sin{\:x}+\sin{\:x}+C}}}}}}}Unchecked
\large x\cdot\sin{\:x}-{{{{{{{\displaystyle\int\sin{\:x}{\:d}x=x\cdot\sin{\:x}-\left(-\cos\:{x}+C\right)=x\cdot\sin{\:x}+\cos{\:x}+C}}}}}}}Unchecked
\large x\cdot\sin{\:x}-{{{{{{{\displaystyle\int\cos{\:x}{\:d}x=x\cdot\sin{\:x}-\left(-\sin\:{x}+C\right)=x\cdot\sin{\:x}+\sin{\:x}+C}}}}}}}Unchecked