# What is f(x) = int (3x+5)^3-x dx if f(1)=-5 ?

Jan 21, 2018

just integrate

#### Explanation:

$f \left(x\right) = \int \left({\left(3 x + 5\right)}^{3} - x\right) \mathrm{dx}$

$\implies \int {\left(3 x + 5\right)}^{3} \mathrm{dx} - \int x \mathrm{dx}$

$\implies f \left(x\right) = \frac{1}{12} {\left(3 x + 5\right)}^{4} - {x}^{2} / 2 + c$- 1
where c is a constant
now placing $x = 1$ and $f \left(1\right) = - 5$

$\implies - 5 = \frac{1}{12} {\left(3 + 5\right)}^{4} - \frac{1}{2} + c$

find c place it back in equation 1

you can find f(x)
hope u find it helpful :)