What is the integral of ((6x+5)^2) ?

The integral of ((6x+5)^2) is 12x^3+30x^2+25x+C

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integral of ((6x+5)^2)

\int ((6 x + 5)^{2}) d x

12 x^{3} + 30 x^{2} + 25 x + C

Solution steps

\int (6 x + 5)^{2} d x

Expand

(6 x + 5)^{2} : 36 x^{2} + 60 x + 25

= \int 36 x^{2} + 60 x + 25 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 36 x^{2} d x + \int 60 x d x + \int 25 d x

\int 36 x^{2} d x = 12 x^{3}

\int 60 x d x = 30 x^{2}

\int 25 d x = 25 x

= 12 x^{3} + 30 x^{2} + 25 x

Add a constant to the solution

= 12 x^{3} + 30 x^{2} + 25 x + C

\frac{d}{d t} (- e^{t})

2 x^{3} + 3 x^{2} - 12 x + 8

\int_{0}^{\frac{π}{16}} tan (8 x) d x

\int_{- 4}^{4} 4 - ∣ x ∣ d x

What is the integral of ((6x+5)^2) ?
The integral of ((6x+5)^2) is 12x^3+30x^2+25x+C