I have this integral that I don't know how to solve:
∫ (x-3)/sqrt(x)
Would I multiply both parentheses first?
or just turn it into (x-3)(x^-0.5)?
integral (x^.5)dx - 3 integral x^(-.5)dx
thanks!
To solve the given integral ∫(x-3)/√x, it is important to simplify the expression before proceeding. In this case, it would be best to multiply the numerator and denominator of the integrand by √x.
Here's how you can do it:
1. Write the expression as ∫(x-3) / (√x * 1).
2. Multiply both the numerator and denominator by the conjugate of the denominator (√x):
∫ (x-3) * (√x) / (√x * √x)
Simplifying it further, you get:
∫ (x√x - 3√x) / x
Now that you have simplified the integrand, you can proceed with integrating it.