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Beliebt Rechnen >

integral of (5x+3-xsec^2(x))/x

Lösung

\int \frac{5 x + 3 - x sec ^{2} ( x )}{x} d x

Lösung

5 x + 3 ln ∣ x ∣ - tan (x) + C

Schritte zur Lösung

\int \frac{5 x + 3 - x sec ^{2} ( x )}{x} d x

Multipliziere aus

\frac{5 x + 3 - x sec ^{2} ( x )}{x} : 5 + \frac{3}{x} - sec^{2} (x)

= \int 5 + \frac{3}{x} - sec^{2} (x) 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 5 d x + \int \frac{3}{x} d x - \int sec^{2} (x) d x

\int 5 d x = 5 x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

\int sec^{2} (x) d x = tan (x)

= 5 x + 3 ln ∣ x ∣ - tan (x)

Füge eine Konstante zur Lösung hinzu

= 5 x + 3 ln ∣ x ∣ - tan (x) + C

Graph

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