Question

what is a integral of x multiple the square of 2x+1 dx?

Answer 1

integral x(2x+1)^2
=integral x(4x^2+4x+1)
=integral (4x^3 + 4x^2 +4x)
=x^4 + (4/3)x^3 +2x^2 +C, where C is a constant

Answer 2

=integral (4x^3 + 4x^2 +x)
=x^4 + (4/3)x^3 +(1./2)x^2 +C, where C is a constant

Answer 3

the last two steps are wrong. This should be correct

Answer 4

sorry I met the square root not the square i.e. the integral x(2x+1)^0.5 dx

Answer 5

integral x(2x+1)^0.5 dx
=integral (1/2)(2x+1)^(1/2) d(2x+1)
=(1/2)(2/3)(2x+1)^(3/2)
=(1/3)(2x+1)^(3/2) +C

Answer 6

why do u put 1/2 in x?

Answer 7

in step 2

Answer 8

because it replace dx to d(2x+1)which is equal to 2xdx. Comparing this to the original one, We have to cancel the extra 2 so multiply it by 1/2