Question

Evaluate the following integrals by the method of u-substitution. Must show all the steps in order to receive credit. a) (14 points) ?_0^1 x^4 (2 + x^5)^3 dx b) (14 points) ?_e^{e^4} dx / (x?(ln x))

Name: Evaluate the following integrals by the method of u-substitution. Must show all the steps in order to receive credit. a) (14 points) ?0^1 x^4 (2 + x^5)^3 dx b) (14 points) ?e^e^4 dx / (x?(ln x))
Uploaded: 2023-06-14T03:25:15-08:00
Duration: 2 min 53 s
Channel: Madhur L
Description: Evaluate the following integrals by the method of u-substitution. Must show all the steps in order to receive credit. a) (14 points) ?0^1 x^4 (2 + x^5)^3 dx b) (14 points) ?e^e^4 dx / (x?(ln x))

          Evaluate the following integrals by the method of u-substitution. Must show all the steps in order to receive credit. a) (14 points) ?_0^1 x^4 (2 + x^5)^3 dx b) (14 points) ?_e^{e^4} dx / (x?(ln x))

Evaluate the following integrals by the method of u-substitution. Must show all the steps in order to receive credit. a) (14 points) ?0^1 x^4 (2 + x^5)^3 dx b) (14 points) ?e^e^4 dx / (x?(ln x))

Added by Robin M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

06/14/2023

Step 1

Let's set: $$u = 2 + 25x^8$$ Now, we need to find the derivative of $u$ with respect to $x$: $$\frac{du}{dx} = 0 + 200x^7$$ Now, we can solve for $dx$: $$dx = \frac{du}{200x^7}$$ Now, we can substitute $u$ and $dx$ into the integral: Show more…

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Evaluate the following integrals by the method of u-substitution. Must show all the steps in order to receive credit. a) ∫[0 to 1] x^4(2 + x^5)^3 dx b) ∫[e to e^4] dx / (x√(ln x))