Question

Evaluate each indefinite integral. SHOW STEPS

Answer 1

2sin(3x⁴+2)

Explanation:

You want the value of the indefinite integral ...

`\displaystyle\int{24x^3\cos(3x^4+2)}\,dx`

Substitution

Define u=3x⁴+2. Then du=12x³·dx, and the integral becomes ...

`\displaystyle\int{2\cos(u)}\,du=2\sin(u)`

Reversing the substitution, we find the integral to be ...

`\displaystyle\int{24x^3\cos(3x^4+2)}\,dx=\boxed{2\sin(3x^4+2)}`

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Additional comment

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