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Calculus
D, Diff, DSolve, fDiff, FourierCos, FourierSeries, FourierSin, iDiff, iLaplace, Integrate, Laplace, Limit, NIntegrate, pDiff, Product, Series, Sum

Algebra
Apart, Coefficient, Degree, Denominator, Divisors, DivisorSigma, Eval, Expand, Factor, GCD, LCM, PolyDivide, PolyFit, PolyGCD, PolyLCM, PowerExpand, Quotient, Remainder, Sequence, SimplifyPoly, Solve, SolveSystem, Together

Basic
Abs, Arg, Conj, Exp, Hyperbolic Functions, Im, Ln, Log, Re, Trigonometric Functions

CAS
Append, Call, Caps, Char, Choose, Clear, Command, Date, Delete, Extract, Function, Insert, IsList, IsMatrix, IsNumber, IsPoly, Left, Length, List, Matrix, Part, Replace, Reshape, Reverse, Right, Size, Sort, String, Value, Variables

Data
Constant, Finance, HRStoHMS, LoadList, LoadMatrix, Table

Elementary
Binomial, Ceil, Eulerian, Factorial, Floor, fPart, iPart, Mod, Multinomial, nCr, nPr, nRoot, Pochhammer, Round, Sign, Sqrt

Graphing
clip, FullRectSineWave, HalfRectSineWave, SawToothWave, SquareWave, StaircaseWave, TriangleWave

Manual
Code Files, Commands, Creating Scripts, Entering Expressions, Graphing Equations, Include Folder, Lists, Matrices, Strings, Symbols, Time Graphing

Matrix
Cholesky, coFactor, Det, Eigenvalues, Eigenvectors, Identity, Inverse, LUDecomposition, QR, RowReduce, SVD, Transpose

Number
AlternatingSeries, Catalan, cFrac, Convergents, IsPrime, LegendreP, nFactors, nPrimes, Pi_Digits, Random

Plot
BodePlot, ContourPlot, CylindricalPlot3D, FractalPlot, ImagePlot, ImplicitPlot, JuliaPlot, ListPlot, ListPlot3D, MultiPlot, MultiPlot3D, ParametricPlot, ParametricPlot3D, Plot, Plot3D, PolarPlot, SphericalPlot3D, VectorPlot, VectorPlot3D

Scripting
Animate, CheckBox, Draw, DrawColor, DrawWindow, Else If, Error, If, Include, Loop, Message, Scroll, Trace, While

Special
AiryAi, AiryBi, BesselI, BesselJ, BesselK, BesselY, Beta, Chi, Ci, Dawson, DiGamma, DiLog, Dirichlet_Eta, Dirichlet_Lambda, Ei, Erf, Erfc, FresnelCos, FresnelSin, Gamma, Gudermannian, HankelH1, HankelH2, Harmonic, Hypergeom_2F1, invGudermannian, KelvinBei, KelvinBer, KelvinKei, KelvinKer, LambertW, Li, LnGamma, PolyGamma, PolyLog, Psi, RK4, RK45, Shi, Si, Zeta

Special Polynomials
Bernoulli, ChebyshevT, ChebyshevU, Euler, Fibonacci, GegenbauerC, HermiteH, LaguerreL, LegendreQ, Lucas

Statistical
BinomialCDF, BinomialPDF, ChiSquareCDF, ChiSquarePDF, Fcdf, Fpdf, GeoCDF, GeoPDF, InverseNormal, Max, Mean, Min, NormalCDF, NormalPDF, PoissonCDF, PoissonPDF, StandardDeviation, StudentTCDF, StudentTPDF, Variance

Trigonometric
DEGtoDMS, ExpConvert, TrigCollect, TrigConvert, TrigExpand, TrigReduce

Vector Calculus
Angle, Cross, Curl, Divergence, Dot, Duf, Gradient, Hessian, Jacobian, Laplacian, Norm, SurfaceNormal
  
Integrate(f(x), x, [a], [b])
Finds the indefinite integral of the given function.

If parameters a and b are given then Integrate returns the definite integral. You can also use NIntegrate for definite integrals.

Examples  
Simple Integrals










Integrals with trigonometric functions







Integrals with reciprocals












Integrals with polynomials








Integrals with logarithmic functions








Integrals with exponential functions









Integrals with inverse trigonometric functions







Integrals with forced substitution






References
http://mathworld.wolfram.com/IndefiniteIntegral.html
http://en.wikipedia.org/wiki/Integral

Related Functions
NIntegrate



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