What is the integral of 3sin(sqrt(x)) ?

The integral of 3sin(sqrt(x)) is 6(-sqrt(x)cos(sqrt(x))+sin(sqrt(x)))+C

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integral of 3sin(sqrt(x))

\int 3 sin (x) d x

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

Solution steps

\int 3 sin (x) d x

Take the constant out:

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

= 3 \cdot \int sin (x) d x

Apply u-substitution

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

= 3 \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

= 3 \cdot 2 \cdot \int sin (u) u d u

Apply Integration By Parts

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

= 3 \cdot 2 (- u cos (u) - \int - cos (u) d u)

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

= 3 \cdot 2 (- u cos (u) - (- sin (u)))

Substitute back

u = x

= 3 \cdot 2 (- x cos (x) - (- sin (x)))

Simplify

= 6 (- x cos (x) + sin (x))

Add a constant to the solution

= 6 (- x cos (x) + sin (x)) + C

y = 6 tan (x), at x = \frac{π}{6}

\frac{\partial}{\partial x} (x^{y} + ln (z))

n = 1 \sum \infty \frac{5}{n ^{3}}

sec (x) \frac{d y}{d x} = e^{y + s i n (x)}

\int \frac{x}{x ^{2} + 7} d x

What is the integral of 3sin(sqrt(x)) ?
The integral of 3sin(sqrt(x)) is 6(-sqrt(x)cos(sqrt(x))+sin(sqrt(x)))+C