∫e∧(x∧2)dx＝?
非正规作法:
e^a=1+a+(a²)/2!+(a^3)/3!+(a^4)/4!+...+(a^n)/n!
a=x²
e^x²=1+x²+(x^4)/2!+(x^6)/3!+(x^8)/4!+...+(x^2n)/n!
∫(e^x²)dx=∫[1+x²+(x^4)/2!+(x^6)/3!+(x^8)/4!+...+(x^2n)/n!]dx
=x+(x^3)/3+(x^5)/5*2!+(x^7)/7*3!+(x^9)/9*4!+...+[x^(2n+1)]/(2n+1)n!
特别争议之处为式子:[x^(2n+1)]/(2n+1)n!
非正规作法:
e^a=1+a+(a²)/2!+(a^3)/3!+(a^4)/4!+...+(a^n)/n!
a=x²
e^x²=1+x²+(x^4)/2!+(x^6)/3!+(x^8)/4!+...+(x^2n)/n!
∫(e^x²)dx=∫[1+x²+(x^4)/2!+(x^6)/3!+(x^8)/4!+...+(x^2n)/n!]dx
=x+(x^3)/3+(x^5)/5*2!+(x^7)/7*3!+(x^9)/9*4!+...+[x^(2n+1)]/(2n+1)n!
特别争议之处为式子:[x^(2n+1)]/(2n+1)n!
