find $\\int(6x + 5)^{2}dx$.\n$\\int(6x + 5)^{2}dx = 12x^{3}+30x^{2}+25x + c$

find $\\int(6x + 5)^{2}dx$.\n$\\int(6x + 5)^{2}dx = 12x^{3}+30x^{2}+25x + c$

find $\\int(6x + 5)^{2}dx$.\n$\\int(6x + 5)^{2}dx = 12x^{3}+30x^{2}+25x + c$

Answer

Explanation:

Step1: Expand the integrand

$$(6x + 5)^2=36x^2+60x + 25$$

Step2: Integrate term - by - term

Using the power rule for integration $\int x^n dx=\frac{x^{n + 1}}{n+1}+C(n\neq - 1)$:

For $\int36x^2dx$: $$\int36x^2dx=36\times\frac{x^{2+1}}{2 + 1}=36\times\frac{x^3}{3}=12x^3$$
For $\int60xdx$: $$\int60xdx=60\times\frac{x^{1+1}}{1+1}=60\times\frac{x^2}{2}=30x^2$$
For $\int25dx$: $$\int25dx=25x$$

Answer:

$$\int(6x + 5)^2dx=12x^3+30x^2+25x + C$$