integral of 1/(sqrt((x-8)(6-x)))

Lösung

\int \frac{1}{( x - 8 ) ( 6 - x )} d x

arcsin (x - 7) + C

Schritte zur Lösung

\int \frac{1}{( x - 8 ) ( 6 - x )} d x

\frac{1}{( x - 8 ) ( 6 - x )} = \frac{1 - ( x - 8 ) ( 6 - x )}{( x - 8 ) ( 6 - x )} + 1

= \int \frac{1 - ( x - 8 ) ( 6 - x )}{( x - 8 ) ( 6 - x )} + 1 d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{1 - ( x - 8 ) ( 6 - x )}{( x - 8 ) ( 6 - x )} d x + \int 1 d x

\int \frac{1 - ( x - 8 ) ( 6 - x )}{( x - 8 ) ( 6 - x )} d x = arcsin (x - 7) - x

\int 1 d x = x

= arcsin (x - 7) - x + x

Vereinfache

= arcsin (x - 7)

Füge eine Konstante zur Lösung hinzu

= arcsin (x - 7) + C

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

\int \frac{x ^{9} - 3 x ^{4}}{x ^{6}} d x

\int \frac{1}{x ^{7}} - \frac{2}{x ^{6}} + 9 x + 8 d x

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

\int (3 x + 1) e^{- x} d x