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Integral $4^{x^3}+6$

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Factor quadratics

Full solution

Q. Integral

4^{x^3}+6

Rewrite Integral: Rewrite the integral to clarify the expression: $\int(4^{x^3} + 6) \, dx$ .
Separate Parts: Separate the integral into two parts: $\int 4^{x^3} \, dx + \int 6 \, dx$ .
Integrate Constant: Integrate the constant: $\int 6 \, dx = 6x + C$ , where $C$ is the constant of integration.
Substitution for Integral: The integral of $4^{x^3}$ is not a standard integral. We need to use substitution. Let $u = x^3$ , then $du = 3x^2 dx$ .
Correction of Substitution: We made a mistake in the previous step. We need to correct the substitution. Let $u = x^3$ , then $du = 3x^2 dx$ is incorrect because we don't have $x^2$ in our integral. We cannot integrate $4^{x^3}$ using elementary functions.

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