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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int \frac{- x - 1}{x ^{2} + 1} d x

Multipliziere aus

\frac{- x - 1}{x ^{2} + 1} : - \frac{x}{x ^{2} + 1} - \frac{1}{x ^{2} + 1}

Wende die Summenregel an:

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of 20cot^4(x)

\int 20 cot^{4} (x) d x

(\partial)/(\partial x)(10x^3+3x^2y-3y^5)

\frac{\partial}{\partial x} (10 x^{3} + 3 x^{2} y - 3 y^{5})

y^{''}-11y^'+30y=20e^t

y^{^{''}} - 11 y^{^{'}} + 30 y = 20 e^{t}

integral from 0 to 2 of (sin(x)+e^x)

\int_{0}^{2} (sin (x) + e^{x}) d x

integral of (x^2(x^3-2x+1))

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