The integration of the function f(x) = x*√x is ∫xf(x)dx = 2/5x^(5/2) + C.
No, the integration of the function g(x) = √x + 2√x is different from the integration of √x. The integration of g(x) is 2/3x^(3/2) + 2x^(3/2) + C, while the integration of √x is 2/3x^(3/2) + C.
To solve the integration of the function h(x) = x*√(1-x^2), you can use the substitution method. Let u = 1-x^2, du = -2xdx. Then, the integration becomes ∫h(x)dx = -1/2∫√udux = -1/3(1-x^2)^(3/2) + C.
Yes, there are some integration techniques that can be used to solve functions with square roots without using substitution. For example, the substitution method, trigonometric substitution, and integration by parts can be used in certain cases.
Yes, it is possible to find the indefinite integral of the function f(x) = x*√(x-1). Using the substitution method, let u = x-1, du = dx. Then, the integration becomes ∫f(x)dx = ∫(u+1)√udu = 2/5u^(5/2) + 2/3u^(3/2) + C = 2/5(x-1)^(5/2) + 2/3(x-1)^(3/2) + C.