What is the integral of 0.67sin(100pix+pi/3) ?

The integral of 0.67sin(100pix+pi/3) is 0.67(0.00275…sin(314.15926…x)-0.00159…cos(314.15926…x))+C

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integral of 0.67sin(100pix+pi/3)

\int 0.67 sin (100 π x + \frac{π}{3}) d x

0.67 (0.00275 \dots sin (314.15926 \dots x) - 0.00159 \dots cos (314.15926 \dots x)) + C

Solution steps

\int 0.67 sin (100 π x + \frac{π}{3}) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 0.67 \cdot \int sin (100 π x + \frac{π}{3}) d x

Rewrite using trig identities

= 0.67 \cdot \int \frac{3}{2} cos (100 π x) + \frac{1}{2} sin (100 π x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 0.67 (\int \frac{3}{2} cos (100 π x) d x + \int \frac{1}{2} sin (100 π x) d x)

\int \frac{3}{2} cos (100 π x) d x = \frac{3}{200 π} sin (100 π x)

\int \frac{1}{2} sin (100 π x) d x = - \frac{1}{200 π} cos (100 π x)

= 0.67 (\frac{3}{200 π} sin (100 π x) - \frac{1}{200 π} cos (100 π x))

Simplify

0.67 (\frac{3}{200 π} sin (100 π x) - \frac{1}{200 π} cos (100 π x)) : 0.67 (0.00275 \dots sin (314.15926 \dots x) - 0.00159 \dots cos (314.15926 \dots x))

= 0.67 (0.00275 \dots sin (314.15926 \dots x) - 0.00159 \dots cos (314.15926 \dots x))

Add a constant to the solution

= 0.67 (0.00275 \dots sin (314.15926 \dots x) - 0.00159 \dots cos (314.15926 \dots x)) + C

\int ((1 + \frac{1}{x})^{3} (\frac{1}{x ^{2}})) d x

8 + x^{2}

f (t) = - cos (t)

ln (5 - x)

f (x) = \frac{2}{3 + x}

What is the integral of 0.67sin(100pix+pi/3) ?
The integral of 0.67sin(100pix+pi/3) is 0.67(0.00275…sin(314.15926…x)-0.00159…cos(314.15926…x))+C