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Beliebt Rechnen >

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

Lösung

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

Lösung

3 x^{2} + 2 x + ln x^{2} + 2 x + x + 1 + C

Schritte zur Lösung

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

Multipliziere aus

\frac{3 x + 4}{2 x + x ^{2}} : \frac{3 x}{2 x + x ^{2}} + \frac{4}{2 x + x ^{2}}

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

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

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

= 3 (x^{2} + 2 x - ln x^{2} + 2 x + x + 1) + 4 ln x^{2} + 2 x + x + 1

Vereinfache

3 (x^{2} + 2 x - ln x^{2} + 2 x + x + 1) + 4 ln x^{2} + 2 x + x + 1 : 3 x^{2} + 2 x + ln x^{2} + 2 x + x + 1

= 3 x^{2} + 2 x + ln x^{2} + 2 x + x + 1

Füge eine Konstante zur Lösung hinzu

= 3 x^{2} + 2 x + ln x^{2} + 2 x + x + 1 + C

Graph

Beliebte Beispiele

integral of \sqrt[3]{x-1}

\int 3 x - 1 d x

derivative (y^3)/3+1/(4y)

d er i v a t i v e \frac{y ^{3}}{3} + \frac{1}{4 y}

integral from 4 to 5 of (sqrt(x-4))/x

\int_{4}^{5} \frac{x - 4}{x} d x

(\partial)/(\partial x)(x^2+3xy+y^2+1)

\frac{\partial}{\partial x} (x^{2} + 3 x y + y^{2} + 1)

integral of 1/(3-2y)

\int \frac{1}{3 - 2 y} d y