Calculation: definite integral ∫ (1,0) x / 1 + x ^ 2

Calculation: definite integral ∫ (1,0) x / 1 + x ^ 2


∫(0→1)x/(1+x^2)dx
=(1/2)∫(0→1)1/(1+x^2)d(1+x^2)
=(1/2)[ln(1+x^2)]|(0→1)
=(1/2)[ln(1+1)-ln(1+0)]
=ln2/2



∫dx/x^2(1-x^2)


∫ dx/x^2(1-x^2)
=∫1/x^2 dx +∫ 1/(1-x^2) dx
= -1/x + 0.5*∫ 1/(1-x) +1/(1+x) dx
=- 1 / X - 0.5ln | 1-x | + 0.5ln | 1 + X | + C, C is constant

Elden Ring Premiere

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