// Numbas version: exam_results_page_options {"name": "Spesielle integrasjonsregler ubestemte integraler", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Spesielle integrasjonsregler ubestemte integraler", "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "

Finn de ubestemte integralene under.

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Hint: For å skrive inn f.eks. $\\frac{1}{x^3}$ bør man skrive 1/(x^3), for å skrive inn $\\cos^2x$ bør man skrive (cos(x))^2. Bruk C eller c for integrasjonskonstanten.

", "advice": "

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 \\sin(kx) dx =-\\frac{1}{k}\\cos(kx)+C\\] ($k$ er et konstant, $x$ er i radianer)

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\\[ \\int \\cos(kx) dx =\\frac{1}{k}\\sin(kx)+C\\] ($k$ er et konstant, $x$ er i radianer)

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\\[ \\int e^{kx} dx =\\frac{1}{k}e^{kx}+C\\] ($k$ er et konstant)

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\\[ \\int a^{kx} dx =\\frac{a^{kx}}{k\\cdot \\ln(x)}+C\\] ($k$ er et konstant,$a\\neq0$ er et konstant)

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

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

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\\[ \\int \\simplify{{out1}}(\\simplify{{inp1}})d\\simplify{{inp1}}=\\] [[0]]

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

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\\[ \\int \\simplify{{out3}}(\\simplify{{inp1}})d\\simplify{{inp1}}= \\] [[0]]

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\\[ \\simplify{{out3}}(\\simplify{{inp3}})=\\sin(\\var{k3}\\var{inp3})\\]

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\\[ \\int \\simplify{{out3}}(\\simplify{{inp3}})d\\simplify{{inp3}}= \\] [[0]]

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\\[ \\simplify{{out4}}(\\simplify{{inp4}})=\\cos(\\var{k4}\\var{inp4})\\]

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

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\\[ \\simplify{{out6}}(\\simplify{{inp6}})=e^{\\var{k6}\\var{inp6}}\\]

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\\[ \\int \\simplify{{out6}}(\\simplify{{inp6}})d\\simplify{{inp6}}= \\] [[0]]

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\\[ \\simplify{{out8}}(\\simplify{{inp8}})=\\var{a}^{{\\var{k8}\\var{inp8}}}\\]

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\\[ \\int \\simplify{{out8}}(\\simplify{{inp8}})d\\simplify{{inp8}}= \\] [[0]]

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\\[ \\simplify{{out2}}(\\simplify{{inp2}})=\\dfrac{1}{\\var{k2}\\var{inp2}} \\]

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\\[ \\int \\simplify{{out2}}(\\simplify{{inp2}})d\\simplify{{inp2}}= \\][[0]]

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