integral of (x^3+1)/x+sin(x)

Lösung

\int \frac{x ^{3} + 1}{x} + sin (x) d x

\frac{x ^{3}}{3} + ln ∣ x ∣ - cos (x) + C

Schritte zur Lösung

\int \frac{x ^{3} + 1}{x} + sin (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{x ^{3} + 1}{x} d x + \int sin (x) d x

\int \frac{x ^{3} + 1}{x} d x = \frac{x ^{3}}{3} + ln ∣ x ∣

\int sin (x) d x = - cos (x)

= \frac{x ^{3}}{3} + ln ∣ x ∣ - cos (x)

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3} + ln ∣ x ∣ - cos (x) + C

\int a x^{3} + \frac{6}{x ^{2}} d x

\int \frac{cos ^{4} ( x )}{sin ^{4} ( x )} d x

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

\int \frac{1}{x ^{2} - 8 x - 9} d x

\int 3 x^{\frac{1}{2}} + 3 d x