integral of (sin(1+sqrt(x)))/(sqrt(x))

Lösung

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

- 2 cos (1 + x) + C

Schritte zur Lösung

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

Wende die partielle Integration an

= 2 x sin (1 + x) - \int cos (1 + x) d x

\int cos (1 + x) d x = 2 (x sin (1 + x) + cos (1 + x))

= 2 x sin (1 + x) - 2 (x sin (1 + x) + cos (1 + x))

Vereinfache

2 x sin (1 + x) - 2 (x sin (1 + x) + cos (1 + x)) : - 2 cos (1 + x)

= - 2 cos (1 + x)

Füge eine Konstante zur Lösung hinzu

= - 2 cos (1 + x) + C

\int_{x}^{5} sin (t^{3}) d t

\int tan^{4} (9 x) d x

d er i v a t i v e f (x) = \frac{2}{x} - \frac{1}{x ^{2}}

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

t an g e n t f (x) = \frac{x}{1 + x ^{2}}, (2, 0.4)