# Answer to Question #20250 in Calculus for kawalpreet kaur

Question #20250

integration of (e raised to power ax+bx)=4e raised to power 4x+3x square/2

Expert's answer

integration of (e^(ax)+bx)=4e^4x+3x^2/2

we can differentiate both parts

e^(ax)+bx=16e^4x+3x

we use that e^t=sum( i=0 to infinity) t^n/n!

so we have

sum( i=0 to infinity) (ax)^n/n!+bx-3x-16sum(i=0 toinfinity) (4x)^n/2=0 sum( i=0 to infinity) (a^n-16*4^n)*x^n/n!=(3-b)x but it possible

if and only if for n=1 (a^n-16*4^n)=3-band for others (a^n-16*4^n)/n!=0 so a^n-16*4^n=0 for n>1 and n=0 but it mean

a=4*16^(1/n) for n>1 its impossible. there is no such a and b

we can differentiate both parts

e^(ax)+bx=16e^4x+3x

we use that e^t=sum( i=0 to infinity) t^n/n!

so we have

sum( i=0 to infinity) (ax)^n/n!+bx-3x-16sum(i=0 toinfinity) (4x)^n/2=0 sum( i=0 to infinity) (a^n-16*4^n)*x^n/n!=(3-b)x but it possible

if and only if for n=1 (a^n-16*4^n)=3-band for others (a^n-16*4^n)/n!=0 so a^n-16*4^n=0 for n>1 and n=0 but it mean

a=4*16^(1/n) for n>1 its impossible. there is no such a and b

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