6.302 и 6.306 6.306 начал вот, но не знаю хелпаните

6.302

$\int { \frac{ x dx }{ ch^2{x} } } = \int { x } \, \frac{dx}{ ch^2{x} } = \int{x} \, dth{x} = x th{x} - \int{ th{x} } \, dx \ = \\\\ = x th{x} - \int{ \frac{ sh{x} }{ ch{x} } } \, dx = x th{x} - \int{ \frac{1}{ ch{x} } } \, sh{x}dx = \\\\ = x th{x} - \int{ \frac{ dch{x} }{ ch{x} } } = x th{x} - \ln{|ch{x}|} \ ;$

6.306

$\int { \frac{ e^x dx }{ e^{2x} + 4e^x - 5 } } = \int { \frac{ de^x }{ (e^x)^2 - [1-5]e^x + [1][-5] } } = \int { \frac{ de^x }{ ( e^x - 1 ) ( e^x + 5 ) } } = \\\\ = \frac{1}{6} \int { ( \frac{ 1 }{ e^x - 1 } - \frac{ 1 }{ e^x + 5 } ) } \, de^x = \frac{1}{6} ( \int { \frac{ d(e^x-1) }{ e^x - 1 } } - \int { \frac{ d(e^x+5) }{ e^x + 5 } } ) = \\\\ = \frac{1}{6} ( \ln{|e^x-1|} - \ln{|e^x+5|} ) = \frac{1}{6} \ln{\frac{ |e^x-1| }{ |e^x+5| } } \ ;$