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solve this: integrate (2x * e ^ x - 3e ^ x)/(sqrt((x ^ 2 - 3x + 6) - 15/4)) dx

Sagot :

Rronoronoidn

Answer:

dx = (2/2) du:

∫ (2 * e^sqrt(u) - 3

Step-by-step explanation:

This is an integration problem and can be solved using integration by substitution. Let's let u = x^2 - 3x + 6 - 15/4, then du = 2x - 3 dx.

Substituting these values into the integral, we get:

∫ (2x * e^x - 3e^x) / (sqrt(u)) du

Now, we need to substitute back, using u = x^2 - 3x + 6 - 15/4 and dx = (2/2) du:

∫ (2 * e^sqrt(u) - 3