Calculate the integral and write the answer in simplest form. int(-2+5x^(4))dx Answer:

Split Integral: We have the integral: int(-2 + 5x^4)dx We can split this integral into two separate integrals: int(-2)dx + int(5x^4)dxIntegrate Terms: Now we integrate each term separately. The integral of a constant -2 with respect to x is -2x. The integral of 5x^4 with respect to x is 5 times the integral of x^4, which is (5/5)x^(4+1)/(4+1) = x^5. So we have: -2x + x^5 + C, where C is the constant of integration.Combine Final Answer: We combine the terms to write the final answer in its simplest form: -2x + x^5 + C

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Find indefinite integrals using the substitution

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Q. Calculate the integral and write the answer in simplest form.

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\int\left(-2+5 x^{4}\right) d x

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Answer:

Split Integral: We have the integral: $\newline$ $\int(-2 + 5x^4)\,dx$ $\newline$ We can split this integral into two separate integrals: $\newline$ $\int(-2)\,dx + \int(5x^4)\,dx$
Integrate Terms: Now we integrate each term separately. $\newline$ The integral of a constant $-2$ with respect to $x$ is $-2x$ . $\newline$ The integral of $5x^4$ with respect to $x$ is $5$ times the integral of $x^4$ , which is $(5/5)x^{(4+1)}/(4+1) = x^5$ . $\newline$ So we have: $\newline$ $-2x + x^5 + C$ , where $C$ is the constant of integration.
Combine Final Answer: We combine the terms to write the final answer in its simplest form: $-2x + x^5 + C$