Question

С подробным решением

Answer 1

$int frac{xdx}{1 + {x}^{2} } = int frac{ frac{1}{2} cdot( 2xdx)}{1 + {x}^{2} } = \ = int frac{ frac{1}{2} d(1 + {x}^{2}) }{1 + {x}^{2} } = \ = frac{1}{2} ln |1 + {x}^{2} | + c = \ = frac{1}{2} ln (1 + {x}^{2} ) + c$