求∫4/(x^2+4)dx

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求∫4/(x^2+4)dx
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求∫4/(x^2+4)dx
求∫4/(x^2+4)dx

求∫4/(x^2+4)dx
∫4/(x^2+4)dx
=∫1/((x/2)^2+1)dx
=2∫1/((x/2)^2+1)d(x/2)
=2arctan(x/2)+C
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原式 = ∫1/[(x/2)^2+1)dx = 2 ∫1/[(x/2)^2+1)d(x/2) = 2arctan(x/2)+c