Answer to Question #174614 in Calculus for Phyroe

Question

Evaluate the integral of (5x+2)³ dx

Answer 1

Answer:

$\int (5x+2)^3dx=\dfrac{1}{20}(5x+ 2)^4+C$

Explanation:

$\int (5x+2)^3dx =$

Making the substitution,

$v =5x+2$, $\dfrac{dv}{dx} =5$

$dx = \dfrac{dv}5$

then,

$\int{(5x+2)^3}dx = \int v³\ \dfrac{dv}{5} = \dfrac15\int v³\ dv$

$= \dfrac15(\dfrac{v⁴}{4}) + C = \dfrac{v⁴}{20} + C$

Since, $v = 5x + 2$

$\therefore \int (5x+2)^3dx=\dfrac{1}{20}(5x+ 2)^4+C$