@_noconds_(True)
def _sine_cosine_transform(f, x, k, a, b, K, name, simplify=True):
 F = integrate(((a * f) * K(((b * x) * k))), (x, 0, oo))
 if (not F.has(Integral)):
  return (_simplify(F, simplify), True)
 if (not F.is_Piecewise):
  raise IntegralTransformError(name, f, 'could not compute integral')
 (F, cond) = F.args[0]
 if F.has(Integral):
  raise IntegralTransformError(name, f, 'integral in unexpected form')
 return (_simplify(F, simplify), cond)

@ _noconds_ ( True ) def _sine_cosine_transform ( f , x , k , a , b , K , name , simplify = True ) : F = integrate ( ( ( a * f ) * K ( ( ( b * x ) * k ) ) ) , ( x , 0 , oo ) ) if ( not F . has ( Integral ) ) : return ( _simplify ( F , simplify ) , True ) if ( not F . is_Piecewise ) : raise IntegralTransformError ( name , f , 'could not compute integral' ) ( F , cond ) = F . args [ 0 ] if F . has ( Integral ) : raise IntegralTransformError ( name , f , 'integral in unexpected form' ) return ( _simplify ( F , simplify ) , cond )
compute a general sine or cosine-type transform f(k) = a int_0^oo b*sin f(x) dx .