What is the integral of 11/4 cos(7/8 x+23) ?

The integral of 11/4 cos(7/8 x+23) is 22/7 sin(7/8 x+23)+C

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integral of 11/4 cos(7/8 x+23)

\int \frac{11}{4} cos (\frac{7}{8} x + 23) d x

\frac{22}{7} sin (\frac{7}{8} x + 23) + C

Solution steps

\int \frac{11}{4} cos (\frac{7}{8} x + 23) d x

Take the constant out:

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

= \frac{11}{4} \cdot \int cos (\frac{7}{8} x + 23) d x

Apply u-substitution

: \int cos (u) \frac{8}{7} d u

= \frac{11}{4} \cdot \int cos (u) \frac{8}{7} d u

Take the constant out:

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

= \frac{11}{4} \cdot \frac{8}{7} \cdot \int cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= \frac{11}{4} \cdot \frac{8}{7} sin (u)

Substitute back

u = \frac{7}{8} x + 23

= \frac{11}{4} \cdot \frac{8}{7} sin (\frac{7}{8} x + 23)

Simplify

\frac{11}{4} \cdot \frac{8}{7} sin (\frac{7}{8} x + 23) : \frac{22}{7} sin (\frac{7}{8} x + 23)

= \frac{22}{7} sin (\frac{7}{8} x + 23)

Add a constant to the solution

= \frac{22}{7} sin (\frac{7}{8} x + 23) + C

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What is the integral of 11/4 cos(7/8 x+23) ?
The integral of 11/4 cos(7/8 x+23) is 22/7 sin(7/8 x+23)+C