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Beliebt Rechnen >

integral of (xcot^2(x^2))/(csc(x^2))

Lösung

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

Lösung

\frac{1}{2} cos (x^{2}) + \frac{1}{2} ln tan (\frac{x ^{2}}{2}) + C

Schritte zur Lösung

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

Umschreiben mit Hilfe von Trigonometrie-Identitäten

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

Multipliziere aus

\frac{x ( - 1 + csc ^{2} ( x ^{2} ) )}{csc ( x ^{2} )} : - \frac{x}{csc ( x ^{2} )} + x csc (x^{2})

= \int - \frac{x}{csc ( x ^{2} )} + x csc (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 \frac{x}{csc ( x ^{2} )} d x + \int x csc (x^{2}) d x

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

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

= - (- \frac{1}{2} cos (x^{2})) + \frac{1}{2} ln tan (\frac{x ^{2}}{2})

Vereinfache

= \frac{1}{2} cos (x^{2}) + \frac{1}{2} ln tan (\frac{x ^{2}}{2})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} cos (x^{2}) + \frac{1}{2} ln tan (\frac{x ^{2}}{2}) + C

Graph

Beliebte Beispiele

integral of (x^2+9)/x

\int \frac{x ^{2} + 9}{x} d x

integral of 1/(xsqrt(64+9x^2))

\int \frac{1}{x 64 + 9 x ^{2}} d x

integral of t/(sqrt(2t^2+1))

\int \frac{t}{2 t ^{2} + 1} d t

integral of 9/(x^3+x^2)

\int \frac{9}{x ^{3} + x ^{2}} d x

integral of (9x^2-10)/((3x^3-10x)^4)

\int \frac{9 x ^{2} - 10}{( 3 x ^{3} - 10 x ) ^{4}} d x