How do you integrate #(x+3) / sqrt(x) dx#?
Emilia AguilarHave a look:
By signing up, you agree to our Terms of Service and Privacy Policy
Charles AnctilTo integrate ( \frac{x+3}{\sqrt{x}} ) with respect to ( x ), you can use substitution. Let ( u = \sqrt{x} ), then ( x = u^2 ) and ( du = \frac{1}{2\sqrt{x}}dx ). Substituting, the integral becomes:
[ \int \frac{x+3}{\sqrt{x}} , dx = \int \frac{u^2 + 3}{u} \cdot 2u , du ]
[ = \int (2u + \frac{3}{u}) , du ]
[ = \int 2u , du + \int \frac{3}{u} , du ]
[ = u^2 + 3\ln|u| + C ]
[ = x + 3\sqrt{x} + C ]
Where ( C ) is the constant of integration.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
- How do you integrate #int (x^2(x^3 + 1)^3)dx#?
- What is the integral of #int 1/(x^(3/2) + x^(1/2)) dx#?
- How do you find the integral of #int dx/[5x(ln(5x))^2]# from 2 to infinity?
- How do you evaluate the definite integral #int sec^2x/(1+tan^2x)# from #[0, pi/4]#?
- How do you use the properties of summation to evaluate the sum of #Sigma i(i-1)^2# from i=1 to 15?
- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7