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Beliebt Rechnen >

integral of (4/(cos^2(x))-5/(sin^2(x)))

Lösung

\int (\frac{4}{cos ^{2} ( x )} - \frac{5}{sin ^{2} ( x )}) d x

Lösung

4 tan (x) + 5 cot (x) + C

Schritte zur Lösung

\int \frac{4}{cos ^{2} ( x )} - \frac{5}{sin ^{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{4}{cos ^{2} ( x )} d x - \int \frac{5}{sin ^{2} ( x )} d x

\int \frac{4}{cos ^{2} ( x )} d x = 4 tan (x)

\int \frac{5}{sin ^{2} ( x )} d x = - 5 cot (x)

= 4 tan (x) - (- 5 cot (x))

Vereinfache

= 4 tan (x) + 5 cot (x)

Füge eine Konstante zur Lösung hinzu

= 4 tan (x) + 5 cot (x) + C

Graph

Beliebte Beispiele

derivative (1/(y^2)-2/(y^4))(y+8y^3)

d er i v a t i v e (\frac{1}{y ^{2}} - \frac{2}{y ^{4}}) (y + 8 y^{3})

integral from-2 to 3 of (35)/(x^4)

\int_{- 2}^{3} \frac{35}{x ^{4}} d x

(dy)/(dx)=e^{2x}+7y

\frac{d y}{d x} = e^{2 x} + 7 y

tangent y=2x^3-x^2+9,(2,21)

t an g e n t y = 2 x^{3} - x^{2} + 9, (2, 21)

integral of 1/(sqrt(x)-4)

\int \frac{1}{x - 4} d x