integral of (3x+a)sin(x)

Lösung

\int (3 x + a) sin (x) d x

3 (- x cos (x) + sin (x)) - a cos (x) + C

Schritte zur Lösung

\int (3 x + a) sin (x) d x

Multipliziere aus

(3 x + a) sin (x) : 3 x sin (x) + a sin (x)

= \int 3 x sin (x) + a 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 3 x sin (x) d x + \int a sin (x) d x

\int 3 x sin (x) d x = 3 (- x cos (x) + sin (x))

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

= 3 (- x cos (x) + sin (x)) - a cos (x)

Füge eine Konstante zur Lösung hinzu

= 3 (- x cos (x) + sin (x)) - a cos (x) + C

\int x (2 x) d x

\int x_{1} d x

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

\int \frac{2 t}{t ^{2} + 4} d t

\int \frac{2 x ^{2} - 1}{x ^{3} - 5 x ^{2} + 6 x} d x