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Beliebt Rechnen >

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

Lösung

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

Lösung

3 tan (x) - x + C

Schritte zur Lösung

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

Multipliziere aus

\frac{2 + sin ^{2} ( x )}{cos ^{2} ( x )} : \frac{2}{cos ^{2} ( x )} + \frac{sin ^{2} ( x )}{cos ^{2} ( x )}

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

\int \frac{2}{cos ^{2} ( x )} d x = 2 tan (x)

\int \frac{sin ^{2} ( x )}{cos ^{2} ( x )} d x = tan (x) - x

= 2 tan (x) + tan (x) - x

Vereinfache

= 3 tan (x) - x

Füge eine Konstante zur Lösung hinzu

= 3 tan (x) - x + C

Graph

Beliebte Beispiele

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

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