3 + 5

8

RowBox[{57.1, ^, 100}]

4.60904*10^175

Inverse[{{1, 2}, {3, 4}}]

{{-2, 1}, {3/2, -1/2}}

Integrate[Sqrt[x] * Sqrt[1 + x], x]

(1 + x)^(1/2) (x^(1/2)/4 + x^(3/2)/2) - ArcSinh[x^(1/2)]/4

Solve[x^2 + xa, x]

{{x1/2 (-1 - (1 + 4 a)^(1/2))}, {x1/2 (-1 + (1 + 4 a)^(1/2))}}

RowBox[{Plot, [, RowBox[{RowBox[{Sin[x], +, RowBox[{Sin, [, RowBox[{1.6, x}], ]}]}], ,, {x, 0, 40}}], ]}]

[Graphics:HTMLFiles/Predavanje-1_12.gif]

⁃Graphics⁃

Plot3D[Sin[x y], {x, 0, 4}, {y, 0, 4}]

[Graphics:HTMLFiles/Predavanje-1_15.gif]

⁃SurfaceGraphics⁃

Inverse[(3 1)] 2 3

{{3/7, -1/7}, {-2/7, 3/7}}

m = Table[Random[], {500}, {500}] ; 

ListPlot[Abs[Eigenvalues[m]]]

[Graphics:HTMLFiles/Predavanje-1_22.gif]

⁃Graphics⁃

100 !

93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000

N[π, 100]

3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068

Factor[x^99 + y^99]

(x + y) (x^2 - x y + y^2) (x^6 - x^3 y^3 + y^6) (x^10 - x^9 y + x^8 y^2 - x^7 y^3 + x^6 y^4 - ... ^33 y^27 - x^30 y^30 - x^27 y^33 + x^21 y^39 + x^18 y^42 - x^12 y^48 - x^9 y^51 + x^3 y^57 + y^60)

Simplify[%]

x^99 + y^99

PartitionsP[10^9]//Short

1604535084280966883272803902639187467146843944735124720885690668610189731030457526857797923685688339

FindRoot[Cos[x] x + Log[x], {x, 1}]

RowBox[{{, RowBox[{x, , 0.840619}], }}]

NIntegrate[Log[x + Sin[x]], {x, 0, 2}]

0.555889

NSolve[x^5 - 6 x^3 + 8 x + 10, x]

RowBox[{{, RowBox[{RowBox[{{, RowBox[{x, , RowBox[{-, 2.05411}]}], }}], ,, RowBox[{{, ... x[{{, RowBox[{x, , 1.55053}], }}], ,, RowBox[{{, RowBox[{x, , 1.9216}], }}]}], }}]

NMinimize[{Cos[x * y] + x, x^2 + y^2≤10}, {x, y}]

NMinimize[{x + Cos[x y], x^2 + y^2≤10}, {x, y}]

FactorInteger[10^40 - 3]

{{13, 1}, {4787, 1}, {48239, 1}, {5853526052603, 1}, {569085301052150111, 1}}

m = Table[2^i + x^j, {i, 3}, {j, 4}]

{{2 + x, 2 + x^2, 2 + x^3, 2 + x^4}, {4 + x, 4 + x^2, 4 + x^3, 4 + x^4}, {8 + x, 8 + x^2, 8 + x^3, 8 + x^4}}

MatrixForm[m]

( 2 3 4 ) 2 + x 2 + x 2 + x 2 + ... x 4 + x 2 3 4 8 + x 8 + x 8 + x 8 + x

NullSpace[m]

{{x + x^2, -1 - x - x^2, 0, 1}, {x, -1 - x, 1, 0}}

NDSolve[{x''[t] + x[t]^3Sin [t], x[0] x '[0] 0}, x, {t, 0, 50}]

RowBox[{{, RowBox[{{, RowBox[{x, , TagBox[RowBox[{InterpolatingFunction, [, RowBox[{Ro ... wBox[{{, RowBox[{0., ,, 50.}], }}], }}], ,, <>}], ]}], False, Editable -> False]}], }}], }}]

ParametricPlot[Evaluate[{x[t], x '[t]}/.%], {t, 0, 50}]

[Graphics:HTMLFiles/Predavanje-1_53.gif]

⁃Graphics⁃

LegendreQ[3, x]

2/3 - (5 x^2)/2 - 3/4 x (1 - (5 x^2)/3) Log[(1 + x)/(1 - x)]

N[MathieuC[1 + I, 2 I, 3], 50]

RowBox[{3.9251311374125198643497646168158379203627176844794, +, RowBox[{1.8988239115433472411052747971439115776785813553761, , }]}]

Integrate[Sqrt[x] ArcTan[x], x]

-(4 x^(1/2))/3 + 1/3 2^(1/2) ArcTan[(-2^(1/2) + 2 x^(1/2))/2^(1/2)] + 1/3 2^(1/2) ArcTan[(2^(1 ... ) ArcTan[x] - Log[-1 + 2^(1/2) x^(1/2) - x]/(3 2^(1/2)) + Log[1 + 2^(1/2) x^(1/2) + x]/(3 2^(1/2))

Integrate[Log[x] * Exp[-(x^3)], {x, 0, Infinity}]

-1/54 Gamma[1/3] (6 EulerGamma + 3^(1/2) π + 9 Log[3])

Integrate[x * Sin[x^2] Exp[-x], {x, 0, Infinity}]

(2 2^(1/2) HypergeometricPFQ[{1}, {1/4, 3/4}, -1/64] + π^(1/2) (-Cos[1/4] + Sin[1/4]))/(4 2^(1/2))

DSolve[y''[x] + y '[x] + x y[x] 0, y[x], x]

{{y[x] ^(-x/2) AiryAi[-(-1)^(1/3) (1/4 - x)] C[1] + ^(-x/2) AiryBi[-(-1)^(1/3) (1/4 - x)] C[2]}}

Created by Mathematica  (November 7, 2007)