The indefinite integral will be [tex]\int (7x^2+8x-2)dx=\dfrac{7x^3}{3}+4x^2-2x+C)[/tex]
When we integrate any function without the limits then it will be an indefinite integral.
General Formulas and Concepts:
Integration Rule [Reverse Power Rule]:
[tex]\int x^ndx=\dfrac{x^{n+1}}{n+1}}+C[/tex]
Integration Property [Multiplied Constant]:
[tex]\int cf(x)dx=c\int f(x)dx[/tex]
Integration Property [Addition/Subtraction]:
[tex]\int [f(x)\pmg(x)]dx=\int f(x)dx\pm \intg(x)dx[/tex]
[Integral] Rewrite [Integration Property - Addition/Subtraction]:
[tex]\int (7x^2+8x-2)dx=\int 7x^2dx+\int 8xdx -\int 2dx[/tex]
[Integrals] Rewrite [Integration Property - Multiplied Constant]:
[tex]\int (7x^2+8x-2)dx=7 \int x^2dx+ 8 \int xdx -2\int dx[/tex]
[Integrals] Reverse Power Rule:
[tex]\int (7x^2+8x-2)dx= 7(\dfrac{x^3}{3})+8(\dfrac{x^2}{2})-2x+C[/tex]
Simplify:
[tex]\int (7x^2+8x-2)dx= \dfrac{7x^3}{3}+4x^2-2x+C[/tex]
So the indefinite integral will be [tex]\int (7x^2+8x-2)dx= \dfrac{7x^3}{3}+4x^2-2x+C[/tex]
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