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

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Answer 1 · 2016-06-07T08:16:06

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

$int (x+3)^4dx$
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,
$frac{1}{5}(x+3)^5+C$

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