What is the integral of cos(x/(sqrt(2))) ?

The integral of cos(x/(sqrt(2))) is sqrt(2)sin(x/(sqrt(2)))+C

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integral of cos(x/(sqrt(2)))

\int cos (\frac{x}{2}) d x

2 sin (\frac{x}{2}) + C

Solution steps

\int cos (\frac{x}{2}) d x

Apply u-substitution

: \int cos (u) 2 d u

= \int cos (u) 2 d u

Take the constant out:

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

= 2 \cdot \int cos (u) d u

Use the common integral:

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

= 2 sin (u)

Substitute back

u = \frac{x}{2}

= 2 sin (\frac{x}{2})

Add a constant to the solution

= 2 sin (\frac{x}{2}) + C

f (x) = 5 x - x^{2}, (1, 4)

(1 + x) d y - y d x = 0

x \to \infty lim (6^{x})

x \to 0 - lim (f (x))

f (x) = - 3 e^{x + 1}

What is the integral of cos(x/(sqrt(2))) ?
The integral of cos(x/(sqrt(2))) is sqrt(2)sin(x/(sqrt(2)))+C