# Thread: check integral is correct?

1. ## check integral is correct?

could someone check ive done this right.... many thnaks

evaluate

$\displaystyle \int {sin (4x)}{cos (x)} dx$

i have....

$\displaystyle \int\frac{1}{2} {sin (a+b)}{sin (a-b)} dx$

$\displaystyle \int\frac{1}{2} {sin (5x)}{sin (3x)} dx$

$\displaystyle \int\frac{1}{2}\frac {(-cos (5x))}{5}+cos (3x)+c dx$

2. Originally Posted by decoy808
could someone check ive done this right.... many thnaks

evaluate

$\displaystyle \int {sin (4x)}{cos (x)} dx$

i have....

$\displaystyle \int\frac{1}{2} {sin (a+b)}{sin (a-b)} dx$

$\displaystyle \int\frac{1}{2} {sin (5x)}{sin (3x)} dx$

$\displaystyle \int\frac{1}{2}\frac {(-cos (5x))}{5}+cos (3x)+c dx$
Check it here: integrate Sin&#x5b;4x&#x5d; Cos&#x5b;x&#x5d; - Wolfram|Alpha

Click on Show steps.

3. Originally Posted by decoy808
could someone check ive done this right.... many thnaks

evaluate

$\displaystyle \int {sin (4x)}{cos (x)} dx$

i have....

$\displaystyle \int\frac{1}{2}\left( {sin (a+b)}\color{red}+\color{black}{sin (a-b)}\right) dx$

$\displaystyle \int\frac{1}{2}\left( {sin (5x)}\color{red}+\color{black}{sin (3x)}\right) dx$

$\displaystyle \color{red}\int\color{black}\frac{1}{2}\frac {(-cos (5x))}{5}\color{red}+cos (3x)\color{black}+c \color{red}dx$
On your last line, you've integrated the first Sine correctly but not the second one, while not removing the integration and dx symbols