Find the integral of 1 3 ( 6 x &#x2212;<!-- − --> 4

airesex2

airesex2

Answered question

2022-05-03

Find the integral of 1 3 ( 6 x 4 ) 2 with respect to x.

Answer & Explanation

bondekoa6i

bondekoa6i

Beginner2022-05-04Added 8 answers

Since 1 3 is constant with respect to x, move 1 3 out of the integral.
1 3 1 ( 6 x 4 ) 2 d x
The partial fraction decomposition cannot be calculated.
1 3 1 2 2 ( 3 x 2 ) 2 d x
Raise 2 to the power of 2.
1 3 1 4 ( 3 x 2 ) 2 d x
Since 1 4 is constant with respect to x, move 1 4 out of the integral.
1 3 ( 1 4 1 ( 3 x 2 ) 2 d x )
Simplify.
1 12 1 ( 3 x 2 ) 2 d x
Let u=3x-2. Then du=3dx, so 1 3 d u = d x. Rewrite using u and du.
1 12 1 u 2 1 3 d u
Simplify.
1 12 1 3 u 2 d u
Since 1 3 is constant with respect to u, move 1 3 out of the integral.
1 12 ( 1 3 1 u 2 d u )
Simplify the expression.
1 36 u 2 d u
By the Power Rule, the integral of u 2 with respect to u is u 1
1 36 ( u 1 + C )
Simplify.
1 36 u + C
Replace all occurrences of u with 3x-2.
1 36 ( 3 x 2 ) + C

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