I am trying to find the integral to 3 x </mrow> ( x

istupilo8k

istupilo8k

Answered question

2022-05-19

I am trying to find the integral to
3 x ( x + 1 ) 4

Answer & Explanation

Ada Harrington

Ada Harrington

Beginner2022-05-20Added 12 answers

Of course you can use integration by parts! Your calculations are correct, except that 1 / 2 mysteriously became 3 / 2 in the last step, and that you forgot to add C
Also, when you multiply by something with a minus sign, you need to write it as x ( 1 3 ) ( x + 1 ) 3 , not x 1 3 ( x + 1 ) 3 which means something completely different.
To compare your answer with the one from symbolab, note that
x ( x + 1 ) 3 = x + 1 1 ( x + 1 ) 3 = 1 ( x + 1 ) 2 1 ( x + 1 ) 3 .
rs450nigglix2

rs450nigglix2

Beginner2022-05-21Added 3 answers

You can use integration by parts without substitution as below:
3 x ( x + 1 ) 4 d x = x d ( 1 ( x + 1 ) 3 ) = x ( x + 1 ) 3 + d x ( x + 1 ) 3 = x ( x + 1 ) 3 1 2 ( x + 1 ) 2 + C = 3 x + 1 2 ( x + 1 ) 3 + C

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