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