integral of ln(x^7)

Lösung

\int ln (x^{7}) d x

7 x ln (x) - 7 x + C

Schritte zur Lösung

\int ln (x^{7}) d x

Wende die partielle Integration an

= x ln (x^{7}) - \int 7 d x

\int 7 d x = 7 x

= x ln (x^{7}) - 7 x

Wende log Regel an

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

angenommen

x \geq 0

= 7 x ln (x) - 7 x

Füge eine Konstante zur Lösung hinzu

= 7 x ln (x) - 7 x + C

(e^{x} + e^{- x}) \frac{d y}{d x} = y^{2}

\int (2 a x + b) (a x^{2} + b x)^{7} d x

d er i v a t i v e x^{2} 5^{x}

\frac{\partial}{\partial x} (ln (8 x^{2} + y^{2} + 3))

\frac{\partial}{\partial y} (15 x^{2} - 9 x y + 25 y^{2})