## anonymous 5 years ago how to solve ∫sin(5x + 2) dx?

1. anonymous

Do you know how to do u-substitution?

2. anonymous

if u=5x+2, du=5 dx... $\int\limits_{}^{}\sin(u)du$

3. anonymous

sin(nx)dx= -1/n cos(nx)+c

4. anonymous

f'(x)=cos(u)5?

5. anonymous

As an antiderivative, we should be able to differentiate our final answer and obtain the original equation, that is, sin(5x+2). if u = 5x+2 and du = 5dx, we substitute in like this: $1/5\int\limits_{}\sin (u) du$ Note that since du = 5dx, we need to cancel out the 5. Hence the 1/5. The integral of the sine function is -cos. So we have 1/5 (-cos(u)) +c Replacing for u, we have 1/5 -cos(5x+2)+c Now lets differentiate and check our work... 1/5 * 5 * sin(5x+2) + 0 = 1*sin(5x+2) = sin(5x+2)

6. anonymous

thank you :)