integral of (cos(ax)-cos(bx))/(x^2)

Lösung

\int \frac{cos ( a x ) - cos ( b x )}{x ^{2}} d x

- \frac{cos ( a x ) - cos ( b x )}{x} - a Si (a x) + b Si (b x) + C

Schritte zur Lösung

\int \frac{cos ( a x ) - cos ( b x )}{x ^{2}} d x

Wende die partielle Integration an

= - \frac{cos ( a x ) - cos ( b x )}{x} - \int - \frac{- a sin ( a x ) + b sin ( b x )}{x} d x

\int - \frac{- a sin ( a x ) + b sin ( b x )}{x} d x = a Si (a x) - b Si (b x)

= - \frac{cos ( a x ) - cos ( b x )}{x} - (a Si (a x) - b Si (b x))

Vereinfache

= - \frac{cos ( a x ) - cos ( b x )}{x} - a Si (a x) + b Si (b x)

Füge eine Konstante zur Lösung hinzu

= - \frac{cos ( a x ) - cos ( b x )}{x} - a Si (a x) + b Si (b x) + C

\int \frac{x ^{2} - 3 x + 3}{x ^{2} - 3 x + 2} d x

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