private static ExComp TakeAntiDerivativeVarGp(ExComp[] gp, AlgebraComp dVar, ref IntegrationInfo pIntInfo, ref EvalData pEvalData)
{
// For later make a method that makes the appropriate substitutions.
// If the inside of a function isn't just a variable and the derivative
// isn't variable, make the substitution.
// Derivative of nothing is just the variable being integrated with respect to.
if (gp.Length == 0)
{
pEvalData.GetWorkMgr().FromFormatted(WorkMgr.STM + "\\int\\d" + dVar.ToDispString() + "=" + dVar.ToDispString() + WorkMgr.EDM,
"Use the antiderivative power rule.");
return dVar;
}
ExComp atmpt = null;
// Is this a single function? (power included)
if (gp.Length == 1 && gp[0] is AlgebraFunction)
{
if (gp[0] is PowerFunction)
gp[0] = (gp[0] as PowerFunction).ForceCombineExponents();
atmpt = GetIsSingleFunc(gp[0], dVar, ref pEvalData);
if (atmpt != null)
{
pEvalData.AttemptSetInputType(InputType.IntBasicFunc);
return atmpt;
}
if (pIntInfo.ByPartsCount < IntegrationInfo.MAX_BY_PARTS_COUNT && (gp[0] is LogFunction || gp[0] is InverseTrigFunction))
{
string thisStr = GroupHelper.ToAlgTerm(gp).FinalToDispStr();
pIntInfo.IncPartsCount();
atmpt = SingularIntByParts(gp[0], dVar, thisStr, ref pIntInfo, ref pEvalData);
if (atmpt != null)
{
pEvalData.AttemptSetInputType(InputType.IntParts);
return atmpt;
}
}
}
else if (gp.Length == 1 && gp[0] is AlgebraComp)
{
pEvalData.GetWorkMgr().FromFormatted(WorkMgr.STM + "({0}^(1+1))/(1+1)=({0}^2)/(2)" + WorkMgr.EDM,
"Use the antiderivative power rule.", gp[0]);
return AlgebraTerm.FromFraction(new PowerFunction(gp[0], new ExNumber(2.0)), new ExNumber(2.0));
}
else if (gp.Length == 2) // Is this two functions multiplied together?
{
ExComp ad = null;
// Are they two of the common antiderivatives?
if (gp[0] is TrigFunction && gp[1] is TrigFunction && (gp[0] as TrigFunction).GetInnerEx().IsEqualTo(dVar) &&
(gp[0] as TrigFunction).GetInnerEx().IsEqualTo(dVar))
{
if ((gp[0] is SecFunction && gp[1] is TanFunction) ||
(gp[0] is TanFunction && gp[1] is SecFunction))
ad = new SecFunction(dVar);
else if ((gp[0] is CscFunction && gp[1] is CotFunction) ||
(gp[0] is CotFunction && gp[1] is CscFunction))
ad = MulOp.Negate(new CscFunction(dVar));
}
if (ad != null)
{
pEvalData.GetWorkMgr().FromFormatted(WorkMgr.STM + "\\int(" + gp[0].ToAlgTerm().FinalToDispStr() +
gp[1].ToAlgTerm().FinalToDispStr() + ")\\d" + dVar.ToDispString() + "=" +
ad.ToAlgTerm().FinalToDispStr() + WorkMgr.EDM,
"Use the common antiderivative.");
pEvalData.AttemptSetInputType(InputType.IntBasicFunc);
return ad;
}
}
if (pIntInfo.USubCount < IntegrationInfo.MAX_U_SUB_COUNT)
{
pIntInfo.IncSubCount();
atmpt = AttemptUSub(gp, dVar, ref pIntInfo, ref pEvalData);
if (atmpt != null)
{
pEvalData.AttemptSetInputType(InputType.IntUSub);
return atmpt;
}
}
if (gp.Length == 1 || gp.Length == 2)
{
ExComp[] den = GroupHelper.GetDenominator(gp, false);
if (den != null && den.Length == 1)
{
ExComp[] num = GroupHelper.GetNumerator(gp);
if (num.Length == 1)
{
int prePFWorkStepCount = ArrayFunc.GetCount(pEvalData.GetWorkMgr().GetWorkSteps());
atmpt = AttemptPartialFractions(num[0], den[0], dVar, ref pIntInfo, ref pEvalData);
if (atmpt != null)
return atmpt;
pEvalData.GetWorkMgr().PopStepsCount(prePFWorkStepCount);
}
}
}
// Trig substitutions.
int prevTrigSubWorkCount = ArrayFunc.GetCount(pEvalData.GetWorkMgr().GetWorkSteps());
atmpt = (new TrigSubTech()).TrigSubstitution(gp, dVar, ref pEvalData);
if (atmpt != null)
return atmpt;
else
pEvalData.GetWorkMgr().PopSteps(prevTrigSubWorkCount);
if (gp.Length == 2)
{
// Using trig identities to make substitutions.
atmpt = TrigFuncIntegration(gp[0], gp[1], dVar, ref pIntInfo, ref pEvalData);
if (atmpt != null)
return atmpt;
// Integration by parts.
if (pIntInfo.ByPartsCount < IntegrationInfo.MAX_BY_PARTS_COUNT)
{
int prevWorkStepCount = ArrayFunc.GetCount(pEvalData.GetWorkMgr().GetWorkSteps());
string thisStr = GroupHelper.ToAlgTerm(gp).FinalToDispStr();
pIntInfo.IncPartsCount();
// Is one of these a denominator because if so don't do integration by parts.
if (!(gp[0] is PowerFunction && (gp[0] as PowerFunction).IsDenominator()) && !(gp[1] is PowerFunction && (gp[1] as PowerFunction).IsDenominator()))
{
atmpt = IntByParts(gp[0], gp[1], dVar, thisStr, ref pIntInfo, ref pEvalData);
if (atmpt != null)
{
pEvalData.AttemptSetInputType(InputType.IntParts);
return atmpt;
}
else
pEvalData.GetWorkMgr().PopStepsCount(ArrayFunc.GetCount(pEvalData.GetWorkMgr().GetWorkSteps()) - prevWorkStepCount);
}
}
}
return null;
}
private static ExComp SecTanTrig(SecFunction sf, TanFunction tf, int sp, int tp, AlgebraComp dVar,
ref IntegrationInfo pIntInfo, ref EvalData pEvalData)
{
if (!sf.GetInnerEx().IsEqualTo(tf.GetInnerEx()))
return null;
bool spEven = sp % 2 == 0;
bool tpEven = tp % 2 == 0;
if (!spEven && tp == 1)
{
//ExComp[] gp = new ExComp[] { PowOp.StaticCombine(sf, new Number(sp - 1)), new AlgebraTerm(sf, new MulOp(), tf) };
//return AttemptUSub(gp, dVar, ref pIntInfo, ref pEvalData);
AlgebraComp subInVar = null;
if (sf.Contains(new AlgebraComp("u")) || tf.Contains(new AlgebraComp("u")))
{
if (sf.Contains(new AlgebraComp("w")) || tf.Contains(new AlgebraComp("u")))
subInVar = new AlgebraComp("v");
else
subInVar = new AlgebraComp("w");
}
else
subInVar = new AlgebraComp("u");
string innerStr = "(" + WorkMgr.ToDisp(sf.GetInnerTerm()) + ")";
pEvalData.GetWorkMgr().FromFormatted(WorkMgr.STM + "\\int \\sec^{" + (sp - 1).ToString() + "}" + innerStr +
"sec" + innerStr + "tan" + innerStr + " d" + dVar.ToDispString() + WorkMgr.EDM, "Split the term up.");
ExComp subbedIn = PowOp.StaticCombine(subInVar, new ExNumber(sp - 1));
pEvalData.GetWorkMgr().FromFormatted(WorkMgr.STM + "\\int " + subInVar.ToDispString() + "^{" + (sp - 1).ToString() + "} d" + subInVar.ToDispString() + WorkMgr.EDM,
"Make the substitution " + WorkMgr.STM + subInVar.ToDispString() + "=\\sec" + innerStr + ", d" + subInVar.ToDispString() +
"=sec" + innerStr + "tan" + innerStr + "d" + subInVar.ToDispString());
ExComp antiDeriv = TakeAntiDerivativeVarGp(new ExComp[] { subbedIn }, subInVar, ref pIntInfo, ref pEvalData);
AlgebraTerm subbedBack = antiDeriv.ToAlgTerm().Substitute(subInVar, sf);
pEvalData.GetWorkMgr().FromSides(subbedBack, null, "Sub back in.");
return subbedBack;
}
//else if (!spEven && tpEven && sp > 2)
//{
// ExComp secSubed = PowOp.StaticCombine(
// AddOp.StaticCombine(
// Number.One,
// PowOp.StaticCombine(new TanFunction(sf.InnerEx), new Number(2.0))),
// new Number((sp - 2) / 2));
// ExComp[] gp = new ExComp[] { PowOp.StaticCombine(tf, new Number(tp)), secSubed, PowOp.StaticCombine(sf, new Number(2.0)) };
// return AttemptUSub(gp, dVar, ref pIntInfo, ref pEvalData);
//}
return null;
}