What is the integral of 10sin(sqrt(x)) ?

The integral of 10sin(sqrt(x)) is 20(-sqrt(x)cos(sqrt(x))+sin(sqrt(x)))+C

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integral of 10sin(sqrt(x))

\int 10 sin (x) d x

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

Solution steps

\int 10 sin (x) d x

Take the constant out:

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

= 10 \cdot \int sin (x) d x

Apply u-substitution

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

= 10 \cdot \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

= 10 \cdot 2 \cdot \int sin (u) u d u

Apply Integration By Parts

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

= 10 \cdot 2 (- u cos (u) - \int - cos (u) d u)

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

= 10 \cdot 2 (- u cos (u) - (- sin (u)))

Substitute back

u = x

= 10 \cdot 2 (- x cos (x) - (- sin (x)))

Simplify

= 20 (- x cos (x) + sin (x))

Add a constant to the solution

= 20 (- x cos (x) + sin (x)) + C

x \to 2 + lim (\frac{x}{∣ x ∣})

(- 45) (- 4 - 8)

f (x) = - \frac{3}{e ^{3 x}}, x = 0

\int e^{5 x} sin (7 x) d x

\frac{\partial}{\partial x} (\frac{1}{x} + \frac{1}{y} + x y)

What is the integral of 10sin(sqrt(x)) ?
The integral of 10sin(sqrt(x)) is 20(-sqrt(x)cos(sqrt(x))+sin(sqrt(x)))+C