What is the integral of cos(x/7) ?

The integral of cos(x/7) is 7sin(x/7)+C

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integral of cos(x/7)

\int cos (\frac{x}{7}) d x

7 sin (\frac{x}{7}) + C

Solution steps

\int cos (\frac{x}{7}) d x

Apply u-substitution

: \int cos (u) \cdot 7 d u

= \int cos (u) \cdot 7 d u

Take the constant out:

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

= 7 \cdot \int cos (u) d u

Use the common integral:

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

= 7 sin (u)

Substitute back

u = \frac{x}{7}

= 7 sin (\frac{x}{7})

Add a constant to the solution

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

2 y^{^{''}} + 3 y^{^{'}} - 2 y = 2 x - 3

y^{^{''}} - 8 y^{^{'}} + 16 y = t^{- 4} e^{4 t}

\int_{1}^{2} 5 x^{2} ln (x) d x

f (x) = 6 x^{\frac{1}{2}}

y = 12 x^{2} - 7 x - 2 x^{- 2}