Question

why anyone is not giving my answers just help me

Answer 1

GOOD MORNING!!

1) integration of a³ log x dx is

=>

a³ integration log(x) dx

=>

a³ × { xlog(x) - x }

Where c is constant of integration.

2)

integration of 2x Sin ( x² + 1 ) dx

=>

Put x² + 1 = z

2x dx = dz

dx = dz/2x

=>

integration of 2x Sin ( z ) × dz/2x

=>

integration of Sin ( z ) dz

=>

-Cos ( z ) + c

where c is called constant of integration.

Now put value of z in -Cos ( z ) we get

-Cos ( x² + 1 ) + c