integral of (x+1)sin(5x)

Lösung

\int (x + 1) sin (5 x) d x

- \frac{1}{5} cos (5 x) (x + 1) + \frac{1}{25} sin (5 x) + C

Schritte zur Lösung

\int (x + 1) sin (5 x) d x

Wende die partielle Integration an

= - \frac{1}{5} cos (5 x) (x + 1) - \int - \frac{1}{5} cos (5 x) d x

\int - \frac{1}{5} cos (5 x) d x = - \frac{1}{25} sin (5 x)

= - \frac{1}{5} cos (5 x) (x + 1) - (- \frac{1}{25} sin (5 x))

Vereinfache

= - \frac{1}{5} cos (5 x) (x + 1) + \frac{1}{25} sin (5 x)

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{5} cos (5 x) (x + 1) + \frac{1}{25} sin (5 x) + C

\frac{d y}{d x} = \frac{cos ( 20 x )}{e ^{20 y}}, y (0) = 2

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

\int \frac{cot ( \frac{x}{2} )}{sin ( x )} d x

d er i v a t i v e f (x) = 8 (4 e^{x} - 26)^{4}

x \to 0 lim ((x - 2)^{5})