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Differentiate w.r.t. x
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\int 6x+2\mathrm{d}y
Evaluate the indefinite integral first.
\left(6x+2\right)y
Find the integral of 6x+2 using the table of common integrals rule \int a\mathrm{d}y=ay.
\left(6x+2\right)\times 6-\left(6x+2\right)z
The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.
2\left(1+3x\right)\left(6-z\right)
Simplify.