Right, or wrong? Say which for each formula and give a brief reason for each answer. int(2x + 1)2 dx =(2x + 1)3/ 3 + C

Caelan 2021-02-20 Answered
Right, or wrong? Say which for each formula and give a brief reason for each answer. (2x+1)2dx=(2x+1)33+C
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Expert Answer

hesgidiauE
Answered 2021-02-21 Author has 106 answers
Step 1
Consider the integral, (2x+1)2dx
Step 2
To solve the given integrals,
(2x+1)2dx=(4x2+1+4x)dx
=4x2dx+1dx+4xdx
=4(x33)+x+4(x22)+C
=4x33+2x2+x+C
Step 3
(2x+1)2dx=(2x+1)332+C
=8x3+1+6x(2x+1)6+C
=8x3+1+12x2+6x6+C
=8x36+12x26+6x6+16+C
=4x33+2x2+x+16+C
Hence the given integral: (2x+1)2dx=(2x+1)33+C is wrong.
The right answer is: (2x+1)2dx=(2x+1)36+C
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