Question

С подробным решением

Answer 1

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