Calculate the integral and write the answer in simplest form. int(3x^(4)-2-5x)dx Answer:

Given Integral: We are given the integral of a polynomial function: int(3x^(4)-2-5x)dx To solve this, we will integrate each term separately.Integrate 3x^4: First, integrate the term 3x^4 with respect to x: int(3x^(4))dx = 3 * int(x^(4))dx = 3 * (x^(4+1)/(4+1)) = 3 * (x^5/5) = (3/5)x^5Integrate -2: Next, integrate the constant term -2 with respect to x: int(-2)dx = -2xIntegrate -5x: Finally, integrate the term -5x with respect to x: int(-5x)dx = -5 * int(x)dx = -5 * (x^(1+1)/(1+1)) = -5 * (x^2/2) = (-5/2)x^2Combine Integrated Terms: Now, combine all the integrated terms to get the final answer: (3/5)x^5 - 2x - (5/2)x^2 + C Here, C represents the constant of integration.

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

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\int\left(3 x^{4}-2-5 x\right) d x

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Answer:

Given Integral: We are given the integral of a polynomial function: $\int(3x^{4}-2-5x)\,dx$ To solve this, we will integrate each term separately.
Integrate $3x^4$ : First, integrate the term $3x^4$ with respect to $x$ : $\int(3x^{4})dx = 3 \times \int(x^{4})dx = 3 \times (x^{4+1}/(4+1)) = 3 \times (x^5/5) = (3/5)x^5$
Integrate $-2$ : Next, integrate the constant term $-2$ with respect to $x$ : $\int(-2)\,dx = -2x$
Integrate $-5x$ : Finally, integrate the term $-5x$ with respect to $x$ : $\int(-5x)\,dx = -5 \times \int(x)\,dx = -5 \times \left(\frac{x^{(1+1)}}{(1+1)}\right) = -5 \times \left(\frac{x^2}{2}\right) = \left(-\frac{5}{2}\right)x^2$
Combine Integrated Terms: Now, combine all the integrated terms to get the final answer: $\newline$ $(\frac{3}{5})x^5 - 2x - (\frac{5}{2})x^2 + C$ $\newline$ Here, $C$ represents the constant of integration.