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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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