Evaluate the indefinite integral. ∫12x2+24xx3+3x2+2

Algotssleeddynf

Algotssleeddynf

Answered

2021-12-29

Evaluate the indefinite integral.
12x2+24xx3+3x2+2

Answer & Explanation

Stella Calderon

Stella Calderon

Expert

2021-12-30Added 35 answers

Step 1
Consider the provided indefinite integral,
Simplify the given indefinite integral as follows,
12x2+24xx3+3x2+2
Apply u-substotution,
let u=x3+3x2+2
dudx=3x2+6x
du=(3x2+6x)dx
multiply 4 in both the sides,
4du=(12x2+24x)dx
Step 2
Now, the given indefinite integral is written as,
12x2+24xx3+3x2+2dx=4duu
=4duu
=4ln|u|+C
Substitute back, u=x3+3x2+2
=4ln|x3+3x2+2|+C
Thus, 12x2+24xx3+3x2+2dx=4ln|x3+3x2+2|+C
Ella Williams

Ella Williams

Expert

2021-12-31Added 28 answers

12x2+24xx3+3x2+2dx
Lets
karton

karton

Expert

2022-01-04Added 439 answers

12x2+24xx3+3x2+2=41udu1udu=ln(u)41udu=ln(u)41udu=4ln(u)=4ln(x3+3x2+2)12x2+24xx3+3x2+2dx=4ln(|x3+3x2+2|)+C

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