de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of 2xsec^2(5x)

Lösung

\int 2 x sec^{2} (5 x) d x

Lösung

x^{2} sec^{2} (5 x) - x^{2} tan^{2} (5 x) + \frac{2}{5} x tan (5 x) + \frac{2}{25} ln ∣ cos (5 x) ∣ - x^{2} + C

Schritte zur Lösung

\int 2 x sec^{2} (5 x) d x

Entferne die Konstante:

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

= 2 \cdot \int x sec^{2} (5 x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= 2 \cdot \int x (1 + tan^{2} (5 x)) d x

Wende die partielle Integration an

= 2 (\frac{1}{2} x^{2} sec^{2} (5 x) - \int 5 x^{2} sec^{2} (5 x) tan (5 x) d x)

\int 5 x^{2} sec^{2} (5 x) tan (5 x) d x = \frac{1}{50} (25 x^{2} tan^{2} (5 x) - 10 x tan (5 x) - 2 ln ∣ cos (5 x) ∣ + 25 x^{2})

= 2 (\frac{1}{2} x^{2} sec^{2} (5 x) - \frac{1}{50} (25 x^{2} tan^{2} (5 x) - 10 x tan (5 x) - 2 ln ∣ cos (5 x) ∣ + 25 x^{2}))

Vereinfache

2 (\frac{1}{2} x^{2} sec^{2} (5 x) - \frac{1}{50} (25 x^{2} tan^{2} (5 x) - 10 x tan (5 x) - 2 ln ∣ cos (5 x) ∣ + 25 x^{2})) : x^{2} sec^{2} (5 x) - x^{2} tan^{2} (5 x) + \frac{2}{5} x tan (5 x) + \frac{2}{25} ln ∣ cos (5 x) ∣ - x^{2}

= x^{2} sec^{2} (5 x) - x^{2} tan^{2} (5 x) + \frac{2}{5} x tan (5 x) + \frac{2}{25} ln ∣ cos (5 x) ∣ - x^{2}

Füge eine Konstante zur Lösung hinzu

= x^{2} sec^{2} (5 x) - x^{2} tan^{2} (5 x) + \frac{2}{5} x tan (5 x) + \frac{2}{25} ln ∣ cos (5 x) ∣ - x^{2} + C

Graph

Beliebte Beispiele

integral of x^2-4x+5

\int x^{2} - 4 x + 5 d x

limit as x approaches 0-of x/(ln(x))

x \to 0 - lim (\frac{x}{ln ( x )})

integral of 1/(8x+5)

\int \frac{1}{8 x + 5} d x

derivative of ln({f}(x)*{f}(x)(sin(x)))

\frac{d}{d x} (ln (f (x)) \cdot f (x) (sin (x)))

integral of (-(2x)/(1+x^2))

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