integral of 1/(xsqrt(1+ln(x^2)))

Lösung

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

1 + 2 ln (x) + C

Schritte zur Lösung

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

Wende U-Substitution an

= \int \frac{1}{2 u} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int \frac{1}{u} d u

Wende die Potenzregel an

= \frac{1}{2} \cdot 2 u^{\frac{1}{2}}

Setze in

u = 1 + ln (x^{2})

ein

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

Vereinfache

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

= 1 + 2 ln (x)

Füge eine Konstante zur Lösung hinzu

= 1 + 2 ln (x) + C

\frac{\partial}{\partial x} (25 - x^{2} - 5 y)

n = 0 \sum \infty \frac{5}{π ^{n}}

\frac{d}{d x} (4 + 2 x - 3 x^{2} - 5 x^{3} - 8 x^{4} + 9 x^{5})

\int_{0}^{2 π} 20 + 16 t^{2} d t

x \to - 2 lim ((x + 1)^{4} (2 x^{2}))