Question

Solve using appropriate methods
∫(x+5)⁻¹ / 2 e^√(x+5)

Answer 1

To solve the integral ∫ (x+5)⁻¹ / 2e^√(x+5), use substitution. Let u = √(x+5) and solve for u. Substitute the value of u back into the original variable, x, to get the final answer.

Step-by-step explanation:

To solve the integral ∫ (x+5)¹⁄₂ / 2e√(x+5), we can use substitution. Let u = √(x+5), therefore du/dx = 1⁄(2√(x+5)). Rearranging the equation, we have dx = 2√(x+5) du. Substituting the values into the integral, it becomes:

∫ (x+5)¹⁄₂ / 2e√(x+5) dx = ∫ u¹⁄₂ / 2eu 2√(x+5) du.

Now, we can simplify the integral and solve for u. Once we have the solution for u, we can substitute it back into the original variable, x, to get the final answer.