Question

how to solve ∫sin(5x + 2) dx?

Answer 1

Do you know how to do u-substitution?

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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)

Answer 6

thank you :)

Answer 7

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