integral of ln(x+(1+x^2)^{1/2})

Lösung

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

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\int x y z^{2} d x

\int sec (x + 1) tan (x + 1) d x

\int x^{2} (x^{3} + 1)^{\frac{1}{4}} d x

\frac{\partial}{\partial t} (2 cos (t))

f (x) = 2 arctan (x)