What is indefinite integral of function f(x) given by f(x)=3x^2+12x+18?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We need to find the indefinite integral of f(x)=3x^2+12x+18

Int [ f(x) dx ]

=> Int [ 3x^2+12x+18 dx ]

=> Int [ 3x^2 dx ] + Int[12x dx] + Int[ 18 dx ]

=> 3*x^3 / 3 + 12x^2 / 2 + 18x + C

=> x^3 + 6x^2 + 18x + C

The indefinite integral of the given function is x^3 + 6x^2 + 18x + C

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

To determine the indefinite integral pf the quadratic function, we'll apply the additive property of integrals:

Int (ax^2 + bx + c)dx = Int ax^2dx + Int bx dx + Int cdx

Comparing, we'll get:

Int (3x^2+12x+18)dx = Int 3x^2dx + Int 12x dx + Int 18dx

Int (3x^2+12x+18)dx = 3*x^3/3 + 12*x^2/2 + 18*x + C

We'll simplify and we'll get:

Int (3x^2+12x+18)dx = x^3 + 6x^2 + 18x + C

The indefinite integral is Int (3x^2+12x+18)dx = x^3 + 6x^2 + 18x + C

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