integral of (4x+7)sin(4x)

Lösung

\int (4 x + 7) sin (4 x) d x

- x cos (4 x) - \frac{7}{4} cos (4 x) + \frac{1}{4} sin (4 x) + C

Schritte zur Lösung

\int (4 x + 7) sin (4 x) d x

Wende die partielle Integration an

= - x cos (4 x) - \frac{7}{4} cos (4 x) - \int - cos (4 x) d x

\int - cos (4 x) d x = - \frac{1}{4} sin (4 x)

= - x cos (4 x) - \frac{7}{4} cos (4 x) - (- \frac{1}{4} sin (4 x))

Vereinfache

= - x cos (4 x) - \frac{7}{4} cos (4 x) + \frac{1}{4} sin (4 x)

Füge eine Konstante zur Lösung hinzu

= - x cos (4 x) - \frac{7}{4} cos (4 x) + \frac{1}{4} sin (4 x) + C

\int sin (2 x) x^{2} d x

\int_{0}^{4} 2 π x (x) d x

\int (6 x)^{3} d x

n = 1 \sum \infty 4^{n} \cdot x^{n}

n = 1 \sum \infty \frac{1}{3 n + 1}