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Find the general indefinite integral. (use c for the constant of integration. )

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The indefinite integral will be  [tex]\int (7x^2+8x-2)dx=\dfrac{7x^3}{3}+4x^2-2x+C)[/tex]

what is indefinite integral?

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]                

To know more about indefinite integral follow

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