2 интеграла...

[esenno_cvete]

1. [tex]\int_{}^{ } \frac{1}{(2\sqrt{x} +3)(3\sqrt{x} -1) }[/tex]dx

2. [tex]\int_{}^{ } (3x^{2} +1)ln(x^{3} +x[/tex])dx

[martin123456]

2
[tex]\int{\ln{(x^3+x)}d(x^3+x)}=\int{\ln{y}dy}=y\ln{y}-\int{yd\ln{y}}=y\ln{y}-y[/tex]

[martin123456]

[tex]-\frac{1}{11}(\frac{2}{2\sqrt{x}+3}-\frac{3}{3\sqrt{x}-1})[/tex]
след полагане [tex]x=y^2[/tex]
[tex]\int{-\frac{1}{11}(\frac{4ydy}{2y+3})}[/tex] е първото [tex]=\int{-\frac{1}{11}\frac{2(2y+3)-6}{2y+3}dy}=\int{-\frac{2}{11}dy}+\int{\frac{6}{11}\frac{dy}{2y+3}}=-\frac{2}{11}y+\frac{3}{11}\int{\frac{d(2y+3)}{2y+3}}=-\frac{2}{11}y+\frac{3}{11}\ln{|2y+3|}[/tex]
другото аналогично