Help with Antiderivative (couple of questions)I am not very good at this and still trying to understand how it works, but I really need to find a antiderivative of x 6 . Would be very glad if someone could help me with that.

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Help with Antiderivative (couple of questions)I am not very good at this and still trying to understand how it works, but I really need to find a antiderivative of       x    6  . Would be very glad if someone could help me with that.

aletantas1x · Accepted Answer

Step 1  ∫      x    6    d  x  =            x      7        7    +  Cbecause       d          d      x            [                  x        7            7        +    C    ]    =            7              x        6              7    +  0  =      x    6  Step 2More generally, for all   n  ≠  −  1,   ∫      x    n    d  x  =            x              n        +        1                    n      +      1        +  C because       d          d      x            [                  x                  n          +          1                            n        +        1              +    C    ]    =            (      n      +      1      )              x        n                    n      +      1        +  0  =      x    n

rigliztetbf · Accepted Answer

Explanation:The antiderivative of   ∫ simply using reverse power rule             x      7        7    +  CThe rule is   ∫       x    n     d  x   =            x              n        +        1                    n      +      1         +  C.

Help with Antiderivative (couple of questions)I am not very good at this and still trying...

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