Identify Function: Identify the function to integrate. We are given the function 8x^2 + 90x to integrate with respect to x.Apply Power Rule: Apply the power rule for integration to each term. The power rule for integration states that the integral of x^n with respect to x is (x^(n+1))/(n+1) + C, where C is the constant of integration.Integrate 8x^2: Integrate the first term 8x^2. Using the power rule, the integral of 8x^2 with respect to x is 8 * (x^(2+1))/(2+1). This simplifies to (8/3)x^3.Integrate 90x: Integrate the second term 90x. Using the power rule, the integral of 90x with respect to x is 90 * (x^(1+1))/(1+1). This simplifies to (90/2)x^2, which is 45x^2.Combine Integrals: Combine the results of the integrals of each term and add the constant of integration. The combined integral of the function 8x^2 + 90x is (8/3)x^3 + 45x^2 + C, where C is the constant of integration.

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integral of $8x^2+90x$

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Q. integral of

8x^2+90x

Identify Function: Identify the function to integrate. $\newline$ We are given the function $8x^2 + 90x$ to integrate with respect to $x$ .
Apply Power Rule: Apply the power rule for integration to each term. $\newline$ The power rule for integration states that the integral of $x^n$ with respect to $x$ is $(x^{(n+1)})/(n+1) + C$ , where $C$ is the constant of integration.
Integrate $8x^2$ : Integrate the first term $8x^2$ . Using the power rule, the integral of $8x^2$ with respect to $x$ is $8 \times (x^{2+1})/(2+1)$ . This simplifies to $(8/3)x^3$ .
Integrate $90x$ : Integrate the second term $90x$ . Using the power rule, the integral of $90x$ with respect to $x$ is $90 \times (x^{1+1})/(1+1)$ . This simplifies to $(90/2)x^2$ , which is $45x^2$ .
Combine Integrals: Combine the results of the integrals of each term and add the constant of integration. $\newline$ The combined integral of the function $8x^2 + 90x$ is $(\frac{8}{3})x^3 + 45x^2 + C$ , where $C$ is the constant of integration.