∫2^x*3^x/(9^x-4^x) dx
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/06 01:08:13
∫2^x*3^x/(9^x-4^x) dx
答案有点出入感觉 ln|(3^x+2^x)/(3^x-2^x)|+C / 2(ln2-ln3)
答案有点出入感觉 ln|(3^x+2^x)/(3^x-2^x)|+C / 2(ln2-ln3)
∫2^x*3^x/(9^x-4^x) dx
= ∫(2/3)^xdx/[1-(4/9)^x]
= [ln(2/3)]^(-1)∫d[(2/3)^x]/{1-[(2/3)^x]^2}
= {[ln(2/3)]^(-1)∫d[(2/3)^x]/[1-(2/3)^x] + [ln(2/3)]^(-1)∫d[(2/3)^x]/[1+(2/3)^x]}/2
= [ln(2/3)]^(-1)[ln|(2/3)^x + 1| - ln|(2/3)^x - 1|]/2
= ∫(2/3)^xdx/[1-(4/9)^x]
= [ln(2/3)]^(-1)∫d[(2/3)^x]/{1-[(2/3)^x]^2}
= {[ln(2/3)]^(-1)∫d[(2/3)^x]/[1-(2/3)^x] + [ln(2/3)]^(-1)∫d[(2/3)^x]/[1+(2/3)^x]}/2
= [ln(2/3)]^(-1)[ln|(2/3)^x + 1| - ln|(2/3)^x - 1|]/2
∫2^x*3^x/(9^x-4^x) dx
∫x^3/9+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
∫(3x^4+x^2)/(x^2+1)dx
∫(x^3-3x^2+4x-9)/(x^2+3)dx
求解微积分题积分题目∫2^x*3^x / (9^x-4^x) dx=?
∫[(x^2-x+6)/(x^3+3x)]dx
∫ [(x^3-2x^2+x+1)/(x^4+5x^2+4)]dx
计算 ∫(x^4-2x^3+x^2+1)/x(x-1)² dx
∫(2^x)/((2^x)+3)dx
∫(x^2+1/x^4)dx