integral of 3sec^3(x)

Lösung

\int 3 sec^{3} (x) d x

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

Schritte zur Lösung

\int 3 sec^{3} (x) d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int sec^{3} (x) d x

Wende integrale Reduktion an

= 3 (\frac{sec ^{2} ( x ) sin ( x )}{2} + \frac{1}{2} \cdot \int sec (x) d x)

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

= 3 (\frac{sec ^{2} ( x ) sin ( x )}{2} + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣)

Vereinfache

3 (\frac{sec ^{2} ( x ) sin ( x )}{2} + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣) : 3 (\frac{1}{2} sec (x) tan (x) + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣)

= 3 (\frac{1}{2} sec (x) tan (x) + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣)

Füge eine Konstante zur Lösung hinzu

= 3 (\frac{1}{2} sec (x) tan (x) + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣) + C

d er i v a t i v e - 7 x^{\frac{2}{3}} - 2 + 3 x^{\frac{7}{4}}

\frac{\partial}{\partial x} ((- y^{2} + x) e^{(x - y)})

d er i v a t i v e f (x) = 2 x^{2} - 196 ln (x)

\int \frac{1}{( 16 - t ^{2} ) ^{\frac{3}{2}}} d t

\int_{- 1}^{3} 30 - 3 y^{2} - \frac{9}{2} d y