What is the integral of sin(sqrt(x)) ?

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

Popular >

integral of sin(sqrt(x))

\int sin (x) d x

2 (- x cos (x) + sin (x)) + C

Solution steps

\int sin (x) d x

Apply u-substitution

: \int sin (u) \cdot 2 u d u

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

Take the constant out:

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

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

Apply Integration By Parts

: - u cos (u) - \int - cos (u) d u

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

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

= 2 (- u cos (u) - (- sin (u)))

Substitute back

u = x

= 2 (- x cos (x) - (- sin (x)))

Simplify

= 2 (- x cos (x) + sin (x))

Add a constant to the solution

= 2 (- x cos (x) + sin (x)) + C

\frac{\partial}{\partial x} (6 x^{7} y^{4} + 2 x^{6} y^{8})

4 y^{3} + 7 x^{8} = 5 y + 6 x, (1, 1)

n = 1 \sum \infty (\frac{5}{2})^{n}

\frac{d}{d x} (\frac{( x ^{3} + 8 )}{2 x})^{7}

u^{6}

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