HOTIcarnt as TIITTS Consider the indefinite integral dx 5+e* The most appropriate substitution to simplify this integral is u = f(x) where f(x) = 5+e* We then have dx = g(u) du where g(u) = %3D Hint: you need to back substitute for x in terms of u for this part. After substituting into the original integral we obtain / h(u) du where h(u) =+C %3D To evaluate this integral rewrite the numerator as 5 = u – (u – 5) simplify, then integrate, thus obtaining | h(u) du = H(u) where H(u) = +C %3D After substituting back for u we obtain our final answer S- dx = + C %3D 5te

Q: Complete the table by identifying u and du for the integral. [ r(g(x))g'(x) dx [x²√x³ +4 dx U = u =…

A:

Q: | sin(6y) sin(8y) dy.

A: we have to solve the integral

Q: Use substitution to find the indefinite integral 25 (5x+1)6 -dx.

A:

Q: Let f f(x)dx = 8 and f(f(x))²dx = 9. Find the following integrals: So cf(z)dz = f(f(x))²dx − (f…

A:

Q: 7-38 Evaluate the integral. 7. X - 1 dx 5x + 1 9. dx (2x + 1)(x – 1) 11 dr

A:

Q: Evaluate the definite integral. (4y° - 3) dy 8. 2. 1 - (4y° - 3) dy = (Simplify your 8. 9. 2. -1

A:

Q: 5 If g(1) = 4, g(5) = -7, and | g(x) dx = -8, evaluate the integral ag (x) dr. Answer:

A:

Q: 2x

A:

Q: The integral sin(x*) dx cannot be evaluated using u-substitution. Explain why, then change the…

A: Consider the given integral: ∫sinx3dx Here, the objective is to change the given integral so that it…

Q: Directions: Evaluate the following definite integral. 1. L,(x- 3x2 + 1)dx 2. L,(x3 – 4x)dx

A: Question 1,Given,           ∫-22x4-3x2+1dx

Q: 1 .2 2 dx = 0 xe 0- -

A: Given: 12π∫-∞∞xe-x22dx=0   We know that; ∫eax+bdx=eax+ba+C     Note: As per Bartleby guidelines we…

Q: Evaluate the indefinite integral. S(52)+4(529)(52+)" dz =

A:

Q: Find the indefinite integral: 2- 2x + x2

A:

Q: 1 dx. VI(x+1)

A: