Question

IDk how tostart please help!
int \frac{ 8dx }{ (4x^2+1)^2 }
int \csc(x) sin(3x) dx

Answer 1

\[\int\limits \frac{ 8dx }{( 4x^2+1)^2 }\]

Answer 2

\[\int\limits \csc(x) \sin(3x)dx\]

Answer 3

for the first one, bring the bottom to the top to get a negative power

then you can just use the trick of
\[\int\limits_{}^{}2(2x+3)^3 dx=\]

would be add one to the power divide by the power, then you also divide by the differential of the inside of the bracket to get

\[\frac{ 2 }{ 4 \times 2 }(2x+3)^{4}\]

Answer 4

use the same logic

Answer 5

@phi

Answer 6

is that easy are you sure ?

Answer 7

yes

Answer 8

what a relief

Answer 9

or you could split into partial fractions

Answer 10

im going to try both methos

Answer 11

why not ?

Answer 12

okay
I will work on the second integral

Answer 13

you can try the partial fraction method if you want

Answer 14

the last one is integrating by parts