integral of 4x^2cos(mx)

Lösung

\int 4 x^{2} cos (m x) d x

4 (\frac{1}{m} x^{2} sin (m x) - \frac{2}{m} (- \frac{1}{m} x cos (m x) + \frac{1}{m ^{2}} sin (m x))) + C

Schritte zur Lösung

\int 4 x^{2} cos (m x) d x

Entferne die Konstante:

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

= 4 \cdot \int x^{2} cos (m x) d x

Wende die partielle Integration an

= 4 (\frac{1}{m} x^{2} sin (m x) - \int \frac{2}{m} x sin (m x) d x)

\int \frac{2}{m} x sin (m x) d x = \frac{2}{m} (- \frac{1}{m} x cos (m x) + \frac{1}{m ^{2}} sin (m x))

= 4 (\frac{1}{m} x^{2} sin (m x) - \frac{2}{m} (- \frac{1}{m} x cos (m x) + \frac{1}{m ^{2}} sin (m x)))

Füge eine Konstante zur Lösung hinzu

= 4 (\frac{1}{m} x^{2} sin (m x) - \frac{2}{m} (- \frac{1}{m} x cos (m x) + \frac{1}{m ^{2}} sin (m x))) + C

\int (7 - \frac{1}{x ^{6}})^{2} (\frac{1}{x ^{7}}) d x

d er i v a t i v e ln (p)

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

\int \frac{t}{t ^{4} + 7} d t

s l o p e (8 - 1) (82)