# How do you integrate #int (x+5)/(2x+3)# using substitution?

We can't immediately substitute into this integrand. First we have to get it into a more receptive form:

We do this with polynomial long division. It's a very simple thing to do on paper but the formatting is quite difficult on here.

By signing up, you agree to our Terms of Service and Privacy Policy

To integrate ∫(x + 5)/(2x + 3) using substitution, you can use the substitution method. Let u = 2x + 3, then du/dx = 2, and dx = du/2. After substituting, the integral becomes ∫(1/2)(x + 5)/u du. Simplify the expression and integrate with respect to u. After integrating, substitute back u = 2x + 3 to express the result in terms of x.

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.

- How do you integrate #(9x)/(9x^2+3x-2)# using partial fractions?
- How do you integrate #int tanx# using substitution?
- How do you integrate #int x^3/sqrt(4x^2+8x+82) dx# using trigonometric substitution?
- How do I find the general antiderivative of #f(x)= sin^2x + cos^2x#?
- How do you integrate by substitution #int (x^2+3x+7)/sqrtxdx#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7