integral of {(3-x)/(x^2+1)+xln(x^2)}

Lösung

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

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

Schritte zur Lösung

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

\int \frac{3 - x}{x ^{2} + 1} d x = 3 arctan (x) - \frac{1}{2} ln x^{2} + 1

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

= 3 arctan (x) - \frac{1}{2} ln x^{2} + 1 + x^{2} ln (x) - \frac{x ^{2}}{2}

Füge eine Konstante zur Lösung hinzu

= 3 arctan (x) - \frac{1}{2} ln x^{2} + 1 + x^{2} ln (x) - \frac{x ^{2}}{2} + C

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

d er i v a t i v e g (x) = x^{2} (1 - 7 x)

\frac{d}{d x} ((\frac{x + 7}{x - 7})^{5})

d er i v a t i v e (x + 3)

x \to 0 + lim (\frac{- 1}{14 x})