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Beliebt Rechnen >

integral of ((r-1))/(sqrt(r^2-4r+3))

Lösung

\int \frac{( r - 1 )}{r ^{2} - 4 r + 3} d r

Lösung

r^{2} - 4 r + 3 + ln r^{2} - 4 r + 3 + r - 2 + C

Schritte zur Lösung

\int \frac{r - 1}{r ^{2} - 4 r + 3} d r

Multipliziere aus

\frac{r - 1}{r ^{2} - 4 r + 3} : \frac{r}{r ^{2} - 4 r + 3} - \frac{1}{r ^{2} - 4 r + 3}

= \int \frac{r}{r ^{2} - 4 r + 3} - \frac{1}{r ^{2} - 4 r + 3} d r

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{r}{r ^{2} - 4 r + 3} d r - \int \frac{1}{r ^{2} - 4 r + 3} d r

\int \frac{r}{r ^{2} - 4 r + 3} d r = r^{2} - 4 r + 3 + 2 ln r^{2} - 4 r + 3 + r - 2

\int \frac{1}{r ^{2} - 4 r + 3} d r = ln r^{2} - 4 r + 3 + r - 2

= r^{2} - 4 r + 3 + 2 ln r^{2} - 4 r + 3 + r - 2 - ln r^{2} - 4 r + 3 + r - 2

Vereinfache

= r^{2} - 4 r + 3 + ln r^{2} - 4 r + 3 + r - 2

Füge eine Konstante zur Lösung hinzu

= r^{2} - 4 r + 3 + ln r^{2} - 4 r + 3 + r - 2 + C

Graph

Beliebte Beispiele

integral of 1/(usqrt(u^2+25))

\int \frac{1}{u u ^{2} + 25} d u

integral of y^4ln(y)

\int y^{4} ln (y) d y

integral of ((x^2)/2)(1/x)

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

integral of (3x+1)/(x^4+3x^2+2)

\int \frac{3 x + 1}{x ^{4} + 3 x ^{2} + 2} d x

integral of 1/((y-2))

\int \frac{1}{( y - 2 )} d y