Question

Find f. Use C for the constant of the first anti derivative and d for the constant of the second derivative

Answer 1

we have the second derivative of the function f(x)

$f^{\doubleprime}(x)=2x+9e^x$

step 1

Find out the first antiderivative of the given function

$f^{\prime}(x)=\int 2x+9e^x=x^2+9e^x+C$

step 2

Find out the second antiderivative

$f(x)=\int x^2+9e^x+C=\frac{x^3}{3}+9e^x+Cx+D$

therefore

$f(x)=\frac{x^3}{3}+9e^x+Cx+D$