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

Lösung

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

x ln (x) - x - ln (x) cos (x) + Ci (x) + C

Schritte zur Lösung

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

Multipliziere aus

(1 + sin (x)) ln (x) : ln (x) + ln (x) sin (x)

= \int ln (x) + ln (x) sin (x) d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int ln (x) d x + \int ln (x) sin (x) d x

\int ln (x) d x = x ln (x) - x

\int ln (x) sin (x) d x = - ln (x) cos (x) + Ci (x)

= x ln (x) - x - ln (x) cos (x) + Ci (x)

Füge eine Konstante zur Lösung hinzu

= x ln (x) - x - ln (x) cos (x) + Ci (x) + C

\int sec^{2} (4 x - 3) d x

\int (x - \frac{1}{x}) x d x

\int \frac{1 + x}{( x ^{2} - 2 x - 3 ) ^{3}} d x

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

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