integral of sec^2(θ)sec(θ)

Lösung

\int sec^{2} (θ) sec (θ) d θ

\frac{1}{2} sec (θ) tan (θ) + \frac{1}{2} ln ∣ tan (θ) + sec (θ) ∣ + C

Schritte zur Lösung

\int sec^{2} (θ) sec (θ) d θ

Vereinfache

sec^{2} (θ) sec (θ) : sec^{3} (θ)

= \int sec^{3} (θ) d θ

Wende integrale Reduktion an

= \frac{sec ^{2} ( θ ) sin ( θ )}{2} + \frac{1}{2} \cdot \int sec (θ) d θ

\int sec (θ) d θ = ln ∣ tan (θ) + sec (θ) ∣

= \frac{sec ^{2} ( θ ) sin ( θ )}{2} + \frac{1}{2} ln ∣ tan (θ) + sec (θ) ∣

Vereinfache

\frac{sec ^{2} ( θ ) sin ( θ )}{2} + \frac{1}{2} ln ∣ tan (θ) + sec (θ) ∣ : \frac{1}{2} sec (θ) tan (θ) + \frac{1}{2} ln ∣ tan (θ) + sec (θ) ∣

= \frac{1}{2} sec (θ) tan (θ) + \frac{1}{2} ln ∣ tan (θ) + sec (θ) ∣

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} sec (θ) tan (θ) + \frac{1}{2} ln ∣ tan (θ) + sec (θ) ∣ + C

\int sin (\frac{2 θ}{3}) d θ

\int x (3 1 - 4 x) d x

\int 3 x^{- \frac{6}{7}} d x

\int 3 - 4 x d x

\int \frac{x}{( 4 + x ^{2} ) ^{2}} d x