integral of (4/(x^2+1)-7/x)

Lösung

\int (\frac{4}{x ^{2} + 1} - \frac{7}{x}) d x

4 arctan (x) - 7 ln ∣ x ∣ + C

Schritte zur Lösung

\int \frac{4}{x ^{2} + 1} - \frac{7}{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 \frac{4}{x ^{2} + 1} d x - \int \frac{7}{x} d x

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

\int \frac{7}{x} d x = 7 ln ∣ x ∣

= 4 arctan (x) - 7 ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= 4 arctan (x) - 7 ln ∣ x ∣ + C

\int \frac{- 5 x}{x ^{2} + 1} d x

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

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

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\int 4 x^{\frac{1}{3}} + 8 x^{- \frac{1}{3}} d x