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INTE.SM
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1993-04-20
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44 lines
output=off
inte(1/x_, x_) := ln(x*sgn(x))
inte(1/sqrt(1-x_^2), x_) := asin(x)
inte(1/sqrt(x_^2-1), x_) := acosh(x)
inte(1/sqrt(1+x_^2), x_) := asinh(x)
inte(sqrt(1+x_^2), x_) := x*sqrt(1+x^2)/2+asinh(x)/2
inte(x_^2*sqrt(1+x_^2), x_) := x*(1+x^2)^1.5/4-sqrt(1+x^2)/8-(1/8)*asinh(x)
inte(sqrt(1+x_^2)/x_, x_) := sqrt(1+x^2)-ln((1+sqrt(1+x^2))/x)
inte(sqrt(1+x_^2)/x_^2, x_) := ln(x+sqrt(1+x^2))-sqrt(1+x^2)/x
inte(sqrt(1-x_^2), x_) := x*sqrt(1-x^2)/2+asin(x)/2
inte(sqrt(x_^2-1), x_) := x*sqrt(x^2-1)/2-acosh(x)/2
inte(abs(x_), x_) := x*abs(x)/2
inte(tan(x_), x_) := ln(sec(x)*sgn(sec(x)))
inte(cot(x_), x_) := ln(sin(x)*sgn(sin(x)))
inte(sec(x_), x_) := ln((sec(x)+tan(x))*sgn(sec(x)+tan(x)))
inte(csc(x_), x_) := ln((csc(x)-cot(x))*sgn(csc(x)-cot(x)))
inte(asin(x_), x_) := x*asin(x)+1/sqrt(1-x^2)
inte(acos(x_), x_) := x*acos(x)-1/sqrt(1-x^2)
inte(atan(x_), x_) := x*atan(x)-ln((1+x^2)*sgn(1+x^2))/2
inte(tanh(x_), x_) := ln(cosh(x)*sgn(cosh(x)))
inte(coth(x_), x_) := ln(sinh(x)*sgn(sinh(x)))
inte(sech(x_), x_) := asin(tanh(x))
inte(csch(x_), x_) := ln((csch(x)-coth(x))*sgn(csch(x)-coth(x)))
inte(sin(x_)^2, x_) := x/2-sin(2*x)/4
inte(cos(x_)^2, x_) := x/2+sin(2*x)/4
inte(tan(x_)^2, x_) := tan(x)-x
inte(cot(x_)^2, x_) := -cot(x)-x
inte(sin(x_)/x_, x_) := si(x)
inte(cos(x_)/x_, x_) := ci(x)
inte(sin(x_)*exp(x_), x_) := (sin(x)-cos(x))*exp(x)/2
inte(cos(x_)*exp(x_), x_) := (sin(x)+cos(x))*exp(x)/2
block(output=on,null)
end