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Finn de bestemte integralene under

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Bruk følgende spesielle integrasjonsregler

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\\[ \\int a dx =ax+C\\]  ($a$ er et konstant)

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\\[ \\int x^n dx =\\frac{1}{n+1}x^{n+1}+C\\]  ($n$ er et reelttall, $n\\neq -1$)

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\\[ \\int \\cos(x) dx =\\sin(kx)+C\\] 

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\\[ \\int \\frac{1}{x} dx =\\ln(x)+C\\] ($k$ er et konstant)

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Bruk analysens fundamentalteorem

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Hvis $f$ og $F$ er kontinuerlige på $[a,b]$ og $F'(x)=f(x)$ for alle $x\\in(a,b)$ så er

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\\[ \\int\\limits_{a}^{b} f(x)dx=F(b)-F(a)

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\\[ \\simplify{{out1}}(\\simplify{{inp1}})=\\var{a} \\]

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\\[ \\int\\limits_{\\var{low1}}^{\\var{up1}} \\simplify{{out1}}(\\simplify{{inp1}})d\\simplify{{inp1}}= \\] [[0]]

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\\[ \\simplify{{out3}}(\\simplify{{inp1}})=\\simplify{{inp1}^{k1}}\\]

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\\[ \\int\\limits_{\\var{low2}}^{\\var{up2}} \\simplify{{out3}}(\\simplify{{inp1}})d\\simplify{{inp1}}= \\] [[0]]

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\\[ \\simplify{{out4}}(\\simplify{{inp4}})=\\cos(\\var{inp4})\\]

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\\[ \\int\\limits_{0}^{\\pi} \\simplify{{out4}}(\\simplify{{inp4}})d\\simplify{{inp4}}= \\] [[0]]

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\\[ \\simplify{{out2}}(\\simplify{{inp2}})=\\dfrac{1}{\\var{inp2}} \\]

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\\[ \\int\\limits_{1}^{e} \\simplify{{out2}}(\\simplify{{inp2}})d\\simplify{{inp2}}= \\][[0]]

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