integral of 2xln(x^2)

Lösung

\int 2 x ln (x^{2}) d x

2 x^{2} ln (x) - x^{2} + C

Schritte zur Lösung

\int 2 x ln (x^{2}) d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int x ln (x^{2}) d x

Wende die partielle Integration an

= 2 (\frac{1}{2} x^{2} ln (x^{2}) - \int x d x)

\int x d x = \frac{x ^{2}}{2}

= 2 (\frac{1}{2} x^{2} ln (x^{2}) - \frac{x ^{2}}{2})

Vereinfache

2 (\frac{1}{2} x^{2} ln (x^{2}) - \frac{x ^{2}}{2}) : 2 x^{2} ln (x) - x^{2}

= 2 x^{2} ln (x) - x^{2}

Füge eine Konstante zur Lösung hinzu

= 2 x^{2} ln (x) - x^{2} + C

\int \frac{cos ^{3} ( x )}{sin ^{2} ( x )} d x

\frac{\partial}{\partial x} ((\frac{x + 2}{y + 1})^{\frac{1}{2}})

l a pl a ce t r an s f or m e^{a s}

n \to \infty lim (- 3 + 4 n^{5})

d er i v a t i v e y = ln (9 x^{2} + 5 y^{2})