integral of 1/(2sqrt(x))arccos(sqrt(x))

Lösung

\int \frac{1}{2 x} arccos (x) d x

x arccos (x) - - x + 1 + C

Schritte zur Lösung

\int \frac{1}{2 x} arccos (x) d x

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int \frac{1}{x} arccos (x) d x

Vereinfache

\frac{1}{x} arccos (x) : \frac{arccos ( x )}{x}

= \frac{1}{2} \cdot \int \frac{arccos ( x )}{x} d x

Wende die partielle Integration an

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

\int - \frac{1}{1 - x} d x = 2 1 - x

= \frac{1}{2} (2 x arccos (x) - 2 1 - x)

Vereinfache

\frac{1}{2} (2 x arccos (x) - 2 1 - x) : x arccos (x) - - x + 1

= x arccos (x) - - x + 1

Füge eine Konstante zur Lösung hinzu

= x arccos (x) - - x + 1 + C

\int \frac{3}{x - x} d x

\int x^{2} \cdot \frac{1}{4 x ^{2} + 9} d x

in t e g r a l x^{2} + x + 1

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

\int \frac{1}{x - 1} d x