integral of w/((1+w)^{3/4)}

Lösung

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

\frac{4}{5} (1 + w)^{\frac{5}{4}} - 4 (1 + w)^{\frac{1}{4}} + C

Schritte zur Lösung

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

Wende U-Substitution an

= \int \frac{u - 1}{u ^{\frac{3}{4}}} d u

Multipliziere aus

\frac{u - 1}{u ^{\frac{3}{4}}} : u^{\frac{1}{4}} - \frac{1}{u ^{\frac{3}{4}}}

= \int u^{\frac{1}{4}} - \frac{1}{u ^{\frac{3}{4}}} d u

Wende die Summenregel an:

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

= \int u^{\frac{1}{4}} d u - \int \frac{1}{u ^{\frac{3}{4}}} d u

\int u^{\frac{1}{4}} d u = \frac{4}{5} u^{\frac{5}{4}}

\int \frac{1}{u ^{\frac{3}{4}}} d u = 4 u^{\frac{1}{4}}

= \frac{4}{5} u^{\frac{5}{4}} - 4 u^{\frac{1}{4}}

Setze in

u = 1 + w

ein

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

Füge eine Konstante zur Lösung hinzu

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

x \to 0 lim (\frac{4}{sin ( 5 x )})

y^{^{'}} = - x e^{- x + y}

\int \frac{( 3 x + 5 )}{x ^{2} + 2 x + 1} d x

\frac{\partial}{\partial x} (x + 4)

x \to 5 lim (- x^{2} + 9 x - 7)