Question

How do you integrate `y=(x+3)^4`?

Answer 1

`frac{1}{5}(x+3)^5+C`

Explanation:

`int (x+3)^4dx`
Applying integral substitution,
`int f(g(x))cdot g^'(x)dx=int f(u)du,quad u=g(x)`
`u=(x+3)quad du=1dx`
`=int u^4du`

Applying power rule,
`int x^adx=frac{x^{a+1}}{a+1},quad ane -1`
`=frac{u^{4+1}}{4+1}`
Substituting back,`u=x+3`
`=frac{(x+3)^{4+1}}{4+1}`

Simplifying it,
`=frac{1}{5}(x+3)^5`

Adding a constant,
`frac{1}{5}(x+3)^5+C`