Answer:
∫((cos(x)*dx)/(√(1+sin(x)))) = 2√(1 + sin(x)) + c.
Step-by-step explanation:
In order to solve this question, it is important to notice that the derivative of the expression (1 + sin(x)) is present in the numerator, which is cos(x). This means that the question can be solved using the u-substitution method.
Let u = 1 + sin(x).
This means du/dx = cos(x). This implies dx = du/cos(x).
Substitute u = 1 + sin(x) and dx = du/cos(x) in the integral.
∫((cos(x)*dx)/(√(1+sin(x)))) = ∫((cos(x)*du)/(cos(x)*√(u))) = ∫((du)/(√(u)))
= ∫(u^(-1/2) * du). Integrating:
(u^(-1/2+1))/(-1/2+1) + c = (u^(1/2))/(1/2) + c = 2u^(1/2) + c = 2√u + c.
Put u = 1 + sin(x). Therefore, 2√(1 + sin(x)) + c. Therefore:
∫((cos(x)*dx)/(√(1+sin(x)))) = 2√(1 + sin(x)) + c!!!
Answer:
your answer is 18
Step-by-step explanation:
Answer:
x = -2
Step-by-step explanation:
3(-2 - 3x) = -9x - 4 (Given)
3(-2) + 3(-3x) = -9x - 4 (Distributive Property of Equality)
-6 + 9x = -9x - 4 (Simplify)
-6 + 4 -9x= -9x - 4 + 4 (Addition Property of Equality)
-2 + 9x = -9x (Simplify)
-2 + 
(Division Property of Equality)
-2 = x (Simplify)
x = -2 (Symmetric Property of Equality)
Answer:
25, 26, 27
Step-by-step explanation:
By adding these three consecutive integers together, you get 78. Test it on a calculator if you'd like to.
