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MaHDaPuH4eG
@MaHDaPuH4eG
March 2022
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Помогите решить. Неопределенный инртеграл
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vasyayu1
4) I(x+1)e^xdx=I(xe^xdx)+I(e^xdx)=xe^x-I(e^xdx)+I(e^xdx)=xe^x+C
5)I(x2^(x^2)dx)=I(2^(x^2)d(x^2))/2=2^(x^2)/(2ln2)
2 votes
Thanks 1
yanaaleksandrov
1. S(x+1)*e^xdx=S(xe^x+e^x)dx=Se^x*xdx+Se^xdx=e^x*x-Se^xdx+Se^xdx=e^x+C
для интеграла e^x: Sfdg=fq-Sqdf, где f=e^x. dq=dx. df=e^xdx. q=x
2. Sx*2^(x^2)dx
для 2^(x^2) u=x^2 du=2xdx S=1/2S2^udu
интеграл от 2^u=2^u/ln2 +C
S=(2^(x^2))/2*ln2 +C=(2^(x^2-1))/ln2 +C
1 votes
Thanks 1
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Answers & Comments
5)I(x2^(x^2)dx)=I(2^(x^2)d(x^2))/2=2^(x^2)/(2ln2)
для интеграла e^x: Sfdg=fq-Sqdf, где f=e^x. dq=dx. df=e^xdx. q=x
2. Sx*2^(x^2)dx
для 2^(x^2) u=x^2 du=2xdx S=1/2S2^udu
интеграл от 2^u=2^u/ln2 +C
S=(2^(x^2))/2*ln2 +C=(2^(x^2-1))/ln2 +C