Question

Use the substitution $u = x^4 - 3$ to evaluate the following indefinite integral. $$ \int \frac{x^3}{x^4 - 3}dx $$

Name: use the substitution u x4 3 to evaluate the following indefinite integral int fracx3x4 3dx 18857
Uploaded: 2020-05-30T23:27:43-08:00
Duration: 1 min 54 s
Channel: Amy Jiang
Description: use the substitution u x4 3 to evaluate the following indefinite integral int fracx3x4 3dx 18857

          Use the substitution $u = x^4 - 3$ to evaluate the following indefinite integral.
$$ \int \frac{x^3}{x^4 - 3}dx $$

$use the substitution u x4 3 to evaluate the following indefinite integral int fracx3x4 3dx 18857$

Added by Stacey R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Amy Jiang

05/30/2020

Step 1

First, we need to find the differential $du$ in terms of $dx$. Given $u = x^4 - 3$. Differentiate both sides with respect to $x$: $$ \frac{du}{dx} = \frac{d}{dx}(x^4 - 3) $$ $$ \frac{du}{dx} = 4x^3 - 0 $$ $$ \frac{du}{dx} = 4x^3 $$ Now, we can write $du$ as: $$ Show more…

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