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Beliebt Rechnen >

integral of (37x+5)/((6x+1)(x-1))

Lösung

\int \frac{37 x + 5}{( 6 x + 1 ) ( x - 1 )} d x

Lösung

\frac{1}{6} ln ∣ 6 x + 1 ∣ + 6 ln ∣ x - 1 ∣ + C

Schritte zur Lösung

\int \frac{37 x + 5}{( 6 x + 1 ) ( x - 1 )} d x

Ermittle den Partialbruch von

\frac{37 x + 5}{( 6 x + 1 ) ( x - 1 )} : \frac{1}{6 x + 1} + \frac{6}{x - 1}

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

\int \frac{1}{6 x + 1} d x = \frac{1}{6} ln ∣ 6 x + 1 ∣

\int \frac{6}{x - 1} d x = 6 ln ∣ x - 1 ∣

= \frac{1}{6} ln ∣ 6 x + 1 ∣ + 6 ln ∣ x - 1 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{1}{6} ln ∣ 6 x + 1 ∣ + 6 ln ∣ x - 1 ∣ + C

Graph

Beliebte Beispiele

derivative f(x)=x*ln(x)

d er i v a t i v e f (x) = x \cdot ln (x)

(\partial)/(\partial x)(x^8+6xy^7)

\frac{\partial}{\partial x} (x^{8} + 6 x y^{7})

derivative 6+1/(x^2)

d er i v a t i v e 6 + \frac{1}{x ^{2}}

y^{''}+4y=3cos(2t)-5sin(2t)

y^{^{''}} + 4 y = 3 cos (2 t) - 5 sin (2 t)

tangent y=x^4-4x^2+10,\at x=1

t an g e n t y = x^{4} - 4 x^{2} + 10, at x = 1