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Beliebt Rechnen >

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

Lösung

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

Lösung

x^{2} + 4 + 2 ln (\frac{1}{2} x + 4 + x^{2}) + C

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

= x^{2} + 4 + 2 ln (\frac{1}{2} x + 4 + x^{2})

Füge eine Konstante zur Lösung hinzu

= x^{2} + 4 + 2 ln (\frac{1}{2} x + 4 + x^{2}) + C

Graph

Beliebte Beispiele

tangent f(x)= 2/x ,\at x=-2

t an g e n t f (x) = \frac{2}{x}, at x = - 2

y^{^{''}} + y = 2^{x}

integral from 1 to 3 of (x^5+1/(4x^5))

\int_{1}^{3} (x^{5} + \frac{1}{4 x ^{5}}) d x

tangent f(x)= 3/x ,(-5,-3/5)

t an g e n t f (x) = \frac{3}{x}, (- 5, - \frac{3}{5})

sum from n=0 to infinity of sin(1/n)

n = 0 \sum \infty sin (\frac{1}{n})