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Beliebt Rechnen >

integral of (2e^{x-3}+3sin(x)+7/(1+x^2))

Lösung

\int (2 e^{x - 3} + 3 sin (x) + \frac{7}{1 + x ^{2}}) d x

Lösung

2 e^{x - 3} - 3 cos (x) + 7 arctan (x) + C

Schritte zur Lösung

\int 2 e^{x - 3} + 3 sin (x) + \frac{7}{1 + x ^{2}} 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 2 e^{x - 3} d x + \int 3 sin (x) d x + \int \frac{7}{1 + x ^{2}} d x

\int 2 e^{x - 3} d x = 2 e^{x - 3}

\int 3 sin (x) d x = - 3 cos (x)

\int \frac{7}{1 + x ^{2}} d x = 7 arctan (x)

= 2 e^{x - 3} - 3 cos (x) + 7 arctan (x)

Füge eine Konstante zur Lösung hinzu

= 2 e^{x - 3} - 3 cos (x) + 7 arctan (x) + C

Graph

Beliebte Beispiele

integral of (sin(7x))/(3cos(7x)+13)

\int \frac{sin ( 7 x )}{3 cos ( 7 x ) + 13} d x

integral of ((sqrt(x)+2)^3)/(2sqrt(x))

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

integral of (3x+7)(-5x-8)

\int (3 x + 7) (- 5 x - 8) d x

integral of e^{2x+x^2}

\int e^{2 x + x^{2}} d x

integral of sqrt(x)+10

\int x + 10 d x