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Beliebt Rechnen >

integral of sin(tan(x))

Lösung

\int sin (tan (x)) d x

Lösung

\frac{1}{4 e} ((e^{2} - 1) Ci (i - tan (x)) + (e^{2} - 1) Ci (tan (x) + i) + i (1 + e^{2}) (Si (i - tan (x)) + Si (tan (x) + i))) + C

Schritte zur Lösung

\int sin (tan (x)) d x

Wende U-Substitution an

= \int \frac{sin ( u )}{1 + u ^{2}} d u

Das ist ein nicht elementares Integral :

\int \frac{sin ( x )}{1 + x ^{2}} d x = \frac{1}{4 e} ((e^{2} - 1) Ci (i - x) + (e^{2} - 1) Ci (x + i) + i (1 + e^{2}) (Si (i - x) + Si (x + i)))

= \frac{1}{4 e} ((e^{2} - 1) Ci (i - u) + (e^{2} - 1) Ci (u + i) + i (1 + e^{2}) (Si (i - u) + Si (u + i)))

Setze in

u = tan (x)

ein

= \frac{1}{4 e} ((e^{2} - 1) Ci (i - tan (x)) + (e^{2} - 1) Ci (tan (x) + i) + i (1 + e^{2}) (Si (i - tan (x)) + Si (tan (x) + i)))

Füge eine Konstante zur Lösung hinzu

= \frac{1}{4 e} ((e^{2} - 1) Ci (i - tan (x)) + (e^{2} - 1) Ci (tan (x) + i) + i (1 + e^{2}) (Si (i - tan (x)) + Si (tan (x) + i))) + C

Beliebte Beispiele

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

\int \frac{x + 1}{x - 1} d x

integral of e^{e^{e^x}}^{e^x}

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

integral of 1/(2+cos^2(x))

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

integral of 2sin(x)-2x^{5/2}+C

\int 2 sin (x) - 2 x^{\frac{5}{2}} + C d x

integral of (6/(5+5x^2))

\int (\frac{6}{5 + 5 x ^{2}}) d x