integral of (ln(y)+2xy^3)

Lösung

\int (ln (y) + 2 x y^{3}) d x

ln (y) x + y^{3} x^{2} + C

Schritte zur Lösung

\int ln (y) + 2 x y^{3} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int ln (y) d x + \int 2 y^{3} x d x

\int ln (y) d x = ln (y) x

\int 2 y^{3} x d x = y^{3} x^{2}

= ln (y) x + y^{3} x^{2}

Füge eine Konstante zur Lösung hinzu

= ln (y) x + y^{3} x^{2} + C

\int_{- 1}^{1} (e^{y} - (y^{2} - 3)) d y

\int (y \cdot e^{x} + sin (y)) d x

\int_{0}^{π} 6 cos^{4} (x) sin (x) d x

x \to - 0.1 lim (1 + e^{x})

4 y - y^{^{''}} = 10 e^{(- 3 x)}