We can pull the constant 6 out of the integral: $$ 6 \int x^2 , dx $$
Depending on the textbook or context, you might see the constant handled differently. Sometimes it is cleaner to define a new constant $A = -C$. Let's look at the result if we clean up the negative sign in the denominator: solve the differential equation. dy dx 6x2y2
integral of 6 x squared space d x equals 6 open paren the fraction with numerator x cubed and denominator 3 end-fraction close paren plus cap C equals 2 x cubed plus cap C So, the equation becomes: negative 1 over y end-fraction equals 2 x cubed plus cap C 4. Solve for Invert both sides to isolate We can pull the constant 6 out of
the fraction with numerator 1 and denominator y squared end-fraction space d y equals 6 x squared space d x 2. Integrate both sides Apply the integral to both sides of the equation: Solve for Invert both sides to isolate the
Multiply both sides by (-1):