Evaluate the integral. int(-30x^(5)+18x^(2))dx Answer:

Given Integral: We are given the integral to evaluate: ∫(-30x^5 + 18x^2)dx We will integrate the function term by term.Integrating -30x^5: First, we integrate the term -30x^5 with respect to x. The antiderivative of x^n is (x^(n+1))/(n+1), so the antiderivative of -30x^5 is: ∫(-30x^5)dx = -30 * (x^(5+1))/(5+1) = -30 * (x^6)/6 Simplifying, we get: -5x^6Integrating 18x^2: Next, we integrate the term 18x^2 with respect to x. The antiderivative of x^n is (x^(n+1))/(n+1), so the antiderivative of 18x^2 is: ∫(18x^2)dx = 18 * (x^(2+1))/(2+1) = 18 * (x^3)/3 Simplifying, we get: 6x^3Combining Results: Now, we combine the results of the two integrals and add the constant of integration C. The final indefinite integral is: -5x^6 + 6x^3 + C

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Q. Evaluate the integral.

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\int\left(-30 x^{5}+18 x^{2}\right) d x

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Answer:

Given Integral: We are given the integral to evaluate: $\int(-30x^5 + 18x^2)dx$ We will integrate the function term by term.
Integrating $-30x^5$ : First, we integrate the term $-30x^5$ with respect to $x$ . The antiderivative of $x^n$ is $(x^{(n+1)})/(n+1)$ , so the antiderivative of $-30x^5$ is: $\int(-30x^5)dx = -30 \cdot (x^{(5+1)})/(5+1) = -30 \cdot (x^6)/6$ Simplifying, we get: $-5x^6$
Integrating $18x^2$ : Next, we integrate the term $18x^2$ with respect to $x$ . The antiderivative of $x^n$ is $(x^{(n+1)})/(n+1)$ , so the antiderivative of $18x^2$ is: $\int(18x^2)dx = 18 \cdot (x^{(2+1)})/(2+1) = 18 \cdot (x^3)/3$ Simplifying, we get: $6x^3$
Combining Results: Now, we combine the results of the two integrals and add the constant of integration $C$ . The final indefinite integral is: $-5x^6 + 6x^3 + C$