The trick here is to use an appropriate substitution. Let u=a^3.
Then du/da=3a^2, and du=3a^2da.
We can now make two key substitutions: In (3a^2)da/(1+a^6), replace 3a^2 by du and a^6 by u^2.
Then we have the integral of du/(1+u^2).
Integrating, we get arctan u + c. Substituting a^3 for u, the final result (the integral in question) is arctan a^3 + c.
Check this by differentiation. if you find the derivative with respect to a of arctan a^3 + c, you MUST obtain the result 3a^2/(1+a^6).
X=6
Isolate the variable by dividing each side by factors that don’t contain variable
Answer:
y= 5/2x - 5
Step-by-step explanation:
5x - 2y = 10
-5x -5x (Subtract both sides by 5x to leave y by itself)
-2y = -5x + 10
-2y/-2 = -5/-2 + 10/-2
(Divide both sides by -2 to leave y with no coefficient. -5/-2 = 5/2 because there are two negatives. 10/-2 = -5.
y = 5/2 - 5
Answer:
-11x+12
Step-by-step explanation:
(x^2-4x+3)-(x^2+7x-9)
x^2-x^2-4x-7x+3-(-9)
-11x+3+9
-11x+12
