1 x² + 8x + 5 x3 + 12x2 + 15x + 6 dx

Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Polynomial And Rational Functions
Section9.2: Remainder And Factor Theorems
Problem 53PS
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Find the indefinite integral.
x² + 8x + 5
1
x3 + 12x2 + 15x + 6
Step 1
du/dx
dx =
1 ½ du
u
Let u = x³ + 12x² + 15x + 6
Begin by rewriting the integral into the following form.
du = 3 x² + 8x +5
3x² +24r + 15
du
x² + 8x + 5
dx =
U1
x³ + 12x² + 15x + 6
3u
Step 2
Solve the new integral using the General Log Rule. Then, back-substitute x into the equation. (Remember to use absolute values where appropriate.)
Si du
du = ln u + C
du
1.
x² + 8x + 5
x3 + 12x² + 15x + 6
U
k
dx =
dx
3
x
³ +12r² + 15z +6
dx
Transcribed Image Text:Find the indefinite integral. x² + 8x + 5 1 x3 + 12x2 + 15x + 6 Step 1 du/dx dx = 1 ½ du u Let u = x³ + 12x² + 15x + 6 Begin by rewriting the integral into the following form. du = 3 x² + 8x +5 3x² +24r + 15 du x² + 8x + 5 dx = U1 x³ + 12x² + 15x + 6 3u Step 2 Solve the new integral using the General Log Rule. Then, back-substitute x into the equation. (Remember to use absolute values where appropriate.) Si du du = ln u + C du 1. x² + 8x + 5 x3 + 12x² + 15x + 6 U k dx = dx 3 x ³ +12r² + 15z +6 dx
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