Mathc initiation/Fichiers c : c77di5
Calculons la primitive :
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Calculer la primitive de | tan(x)**n dx
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| tan(x)**n dx = | tan(x)**(n-2) tan(x)**2 dx
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tan(x)**2 = (sec(x)**2 - 1)
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| tan(x)**(n-2) (sec(x)**2 - 1) dx
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| (tan(x)**(n-2)sec(x)**2 - tan(x)**(n-2)) dx
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| tan(x)**(n-2)sec(x)**2 dx - | tan(x)**(n-2) dx
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^
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u = tan(x)
du = sec(x)**2 dx
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| u**(n-2) du - | tan(x)**(n-2) dx
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1/(n-1) u**(n-1) - | tan(x)**(n-2) dx
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| tan(x)**n dx = ----- (tan(x)**(n-1) - | tan(x)**(n-2) dx
/ (n-1) /