Question

1.Найти неопределенные интегралы.
∫(x^2+ln(x^2))/x

Answer 1

$int frac{ {x}^{2} + ln( {x}^{2} ) }{x} dx = frac{1}{2} int frac{t + ln(t) }{t}dt =\ {x}^{2} = t, : dx = frac{1}{2x} dt \ = frac{1}{2} int1dt + frac{1}{2}intfrac{ ln(t) }{t} dt = frac{t}{2} + frac{1}{2} int frac{ ln(t) }{t} dt = \ ln(t) = u, : dt = tdu \ = frac{t}{2} + frac{1}{2} int udu = frac{t}{2} + frac{ {u}^{2} }{4} = frac{ {x}^{2} }{2} + ln^{2} (x) + C$