Evaluate the integral. (Remember to use absolute values where appropriate.

aidmoong7

aidmoong7

Answered question

2021-12-03

Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)
x4(x+7)(x2)dx

Answer & Explanation

Geraldine Flores

Geraldine Flores

Beginner2021-12-04Added 21 answers

Step 1
Given:
x4(x2)(x+7)dx
Perform partial fraction decomposition:
(119(x+7)29(x2))dx
Apply linearity:
1191x+7dx291x2dx
Now solving 1x+7dx
Substitute u=x+7dudx=1 and dx=du
1udu=ln(u)
Undo the substitution ln(x+7)
Step 2
Similarly for 1x2
u=x2dudx=1du=dx
1udu
ln(u)
Undo the substitution
ln(x2)
Plug in the solved integrals:
1191x+7dx291x2dx
119ln(x+7)29ln(x2)+C
Therefore x4(x2)(x+7)dx=119ln(x+7)29ln(x2)+C

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