Indefinite integralDetermine the indefinite integral of y=6x^5+2x-1 .

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

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We need to find the integral of y = 6x^5 + 2x - 1.

Use the property that the integral for x^n is (1/(n + 1))*x^(n + 1) for each of the terms.

Int[6x^5 + 2x - 1 dx]

=> 6*x^6 / 6 + 2*x^2/2 - x/1 +C

=> x^6 + x^2 - x + C

The required integral of y = 6x^5 + 2x - 1 is  x^6 + x^2 - x + C

 

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll write y = f(x) and we'll compute the indefinite integral of f(x):

Int f(x)dx = Int (6x^5 + 2x -1)dx

We'll apply the property of integral to be additive and we'll get:

Int (6x^5 + 2x -1)dx = Int 6x^5dx + Int 2xdx - Int dx

We'll re-write the sum of integrals:

Int (6x^5 + 2x -1)dx = 6Int x^5dx + 2Int xdx - Int dx

Int (6x^5 + 2x -1)dx = 6*x^6/6 + 2*x^2/2 - x + C

We'll simplify and we'll get the indefinite integral of y=6x^5 + 2x -1:

Int (6x^5 + 2x -1)dx = x^6 + x^2 - x + C

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