integral of 5x*cos(x)

Lösung

\int 5 x \cdot cos (x) d x

5 (x sin (x) + cos (x)) + C

Schritte zur Lösung

\int 5 x cos (x) d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int x cos (x) d x

Wende die partielle Integration an

= 5 (x sin (x) - \int sin (x) d x)

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

= 5 (x sin (x) - (- cos (x)))

Vereinfache

= 5 (x sin (x) + cos (x))

Füge eine Konstante zur Lösung hinzu

= 5 (x sin (x) + cos (x)) + C

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

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

\int \frac{x ^{2} - 2}{x ^{2} - x - 2} d x

\int sec^{- 2} (x) tan^{3} (x) d x

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