integral from 0 to 33 of (x-1)^{-1/5}

Lösung

\int_{0}^{33} (x - 1)^{- \frac{1}{5}} d x

\frac{75}{4}

Dezimale

18.75

Schritte zur Lösung

\int_{0}^{33} (x - 1)^{- \frac{1}{5}} d x

Bestimme unbestimmte (Singularitäts-)Punkte:

x = 1

Wenn

b, a < b < c, f (b) =

unbestimmt

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{0}^{1} (x - 1)^{- \frac{1}{5}} d x + \int_{1}^{33} (x - 1)^{- \frac{1}{5}} d x

\int_{0}^{1} (x - 1)^{- \frac{1}{5}} d x = - \frac{5 ( - 1 ) ^{\frac{4}{5}}}{4}

\int_{1}^{33} (x - 1)^{- \frac{1}{5}} d x = 20

= - \frac{5 ( - 1 ) ^{\frac{4}{5}}}{4} + 20

Vereinfache

- \frac{5 ( - 1 ) ^{\frac{4}{5}}}{4} + 20 : \frac{75}{4}

= \frac{75}{4}

in v erse l a pl a ce \frac{π}{( s ^{2} + π ) ^{2}}

\int \frac{( x ^{2} + 5 )}{x ^{3} - x ^{2} + x + 3} d x

\int (e^{- s x}) d x

t an g e n t y = sin (sin (x)), (4 π, 0)

x \to 0 lim (x^{5 s i n (x)})