integral of (x^3+2/(5-6x)+3cos(5-7x))

Lösung

\int (x^{3} + \frac{2}{5 - 6 x} + 3 cos (5 - 7 x)) d x

\frac{x ^{4}}{4} - \frac{1}{3} ln ∣ 5 - 6 x ∣ - \frac{3}{7} sin (5 - 7 x) + C

Schritte zur Lösung

\int x^{3} + \frac{2}{5 - 6 x} + 3 cos (5 - 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 x^{3} d x + \int \frac{2}{5 - 6 x} d x + \int 3 cos (5 - 7 x) d x

\int x^{3} d x = \frac{x ^{4}}{4}

\int \frac{2}{5 - 6 x} d x = - \frac{1}{3} ln ∣ 5 - 6 x ∣

\int 3 cos (5 - 7 x) d x = - \frac{3}{7} sin (5 - 7 x)

= \frac{x ^{4}}{4} - \frac{1}{3} ln ∣ 5 - 6 x ∣ - \frac{3}{7} sin (5 - 7 x)

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{4}}{4} - \frac{1}{3} ln ∣ 5 - 6 x ∣ - \frac{3}{7} sin (5 - 7 x) + C

\int \frac{- 7 x ^{2} + 2 x - 1}{( x - 1 ) ^{2} ( 3 x - 2 )} d x

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

\int cos (5 x - 2) d x

\int f (a x + b) d x

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