Question

Consider the integral ? 7x^6 ln(x) dx: Applying the integration by parts technique, let u = ln(x) and dv = x^6 dx Then du = 1/x dx and v = x^7/7 Then uv - ? vdu = (x^7 ln(x))/7 - ? x^6/7 dx Integration gives the final answer (x^7 (7 ln(x) - 1))/7

Name: Consider the integral ? 7x^6 ln(x) dx: Applying the integration by parts technique, let u = ln(x) and dv = x^6 dx Then du = 1/x dx and v = x^7/7 Then uv - ? vdu = (x^7 ln(x))/7 - ? x^6/7 dx Integration gives the final answer (x^7 (7 ln(x) - 1))/7
Uploaded: 2023-09-09T17:39:58-08:00
Duration: 2 min 45 s
Channel: Adi S
Description: Consider the integral ? 7x^6 ln(x) dx: Applying the integration by parts technique, let u = ln(x) and dv = x^6 dx Then du = 1/x dx and v = x^7/7 Then uv - ? vdu = (x^7 ln(x))/7 - ? x^6/7 dx Integration gives the final answer (x^7 (7 ln(x) - 1))/7

          Consider the integral ? 7x^6 ln(x) dx: Applying the integration by parts technique, let u = ln(x) and dv = x^6 dx Then du = 1/x dx and v = x^7/7 Then uv - ? vdu = (x^7 ln(x))/7 - ? x^6/7 dx Integration gives the final answer (x^7 (7 ln(x) - 1))/7

Consider the integral ? 7x^6 ln(x) dx: Applying the integration by parts technique, let u = ln(x) and dv = x^6 dx Then du = 1/x dx and v = x^7/7 Then uv - ? vdu = (x^7 ln(x))/7 - ? x^6/7 dx Integration gives the final answer (x^7 (7 ln(x) - 1))/7

Added by Jessica F.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/09/2023

Step 1

First, we have the integral: $$\int x^6 \ln(x) dx$$ We will use integration by parts, which is given by: $$\int u dv = uv - \int v du$$ Let's choose: $$u = \ln(x) \Rightarrow du = \frac{1}{x} dx$$ $$dv = x^6 dx \Rightarrow v = \frac{1}{7}x^7$$ Now, we can apply Show more…

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Consider the integral ∫ ln(w) dx. Applying the integration by parts technique, let u = ln(x) and dv = dx. Then du = (1/x) dx and v = x. Using the integration by parts formula, we have: ∫ ln(w) dx = x ln(w) - ∫ (1/x) x dx. Simplifying further, we get: ∫ ln(w) dx = x ln(w) - ∫ dx. Integrating the second term, we have: ∫ ln(w) dx = x ln(w) - x + C where C is the constant of integration.