∫x^3/(9+x^2)dx

来源：学生作业帮助网 编辑：作业帮 时间：2024/04/29 19:08:18
∫x^3/(9+x^2)dx
x){Ա"X_R"H3&HSPΆX A[C}#B"HAHؖh"+))(L)A(ѶԵ&mk E( ŵ@ G sdoe@'*R*tBE 5B1}nq

∫x^3/(9+x^2)dx
∫x^3/(9+x^2)dx

∫x^3/(9+x^2)dx
∫x^3/(9+x^2)dx
=1/2∫x^2/(9+x^2)dx^2 (x^2=t)
=1/2∫t/(9+t)dt
=1/2∫(t+9-9)/(9+t)dt
=1/2∫[1-9/(9+t)]dt
=1/2t-9/2ln(9+t)+C
=1/2x^2-9/2ln(9+x^2)+C

原式=∫(x-9x/(9+x^2))dx=∫xdx-∫9x/(9+x^2)dx
=x^2/2-9ln(x^2+9)/2+C

∫x^3/9+X^2 dx. ∫3+x/(9-x^2)dx ∫x^3/(9+x^2)dx x-9/[(根号)x]+3 dx ∫ x+1/[(根号)x] dx ∫ [（3-x^2）]^2 dx ∫2^x-3dx 求助∫d/dx[X^tan(x^2)]dx 和 ∫dx/(2+3X^2) ∫x/(4+9x^2)dx ∫dx/x(2x+3)^2 ∫(2^x+3^x)²dx ∫X^2 e^-X^3 dx. ∫（x-3x+2）dx ∫x^3/1+x^2 dx ∫(x-1)^2/x^3 dx ∫dx/(x-2)平方(x-3) ∫(X^3)/(1+X^2)dx ∫x^2/x+3dx ∫x^3*e^x^2dx ∫[(x^2-x+6)/(x^3+3x)]dx