integral of (1+cos^2(θ))/(cos^2(θ))

Lösung

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

tan (θ) + θ + C

Schritte zur Lösung

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

Multipliziere aus

\frac{1 + cos ^{2} ( θ )}{cos ^{2} ( θ )} : \frac{1}{cos ^{2} ( θ )} + 1

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

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{1}{cos ^{2} ( θ )} d θ + \int 1 d θ

\int \frac{1}{cos ^{2} ( θ )} d θ = tan (θ)

\int 1 d θ = θ

= tan (θ) + θ

Füge eine Konstante zur Lösung hinzu

= tan (θ) + θ + C

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