What is the integral of sqrt(18-18sin(x)) ?

The integral of sqrt(18-18sin(x)) is 6sqrt(2)sqrt(sin(x)+1)+C

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integral of sqrt(18-18sin(x))

\int 18 - 18 sin (x) d x

62 sin (x) + 1 + C

Solution steps

\int 18 - 18 sin (x) d x

Factor

18 - 18 sin (x) : - 18 (sin (x) - 1)

= \int - 18 (sin (x) - 1) d x

Simplify

- 18 (sin (x) - 1) : 32 - sin (x) + 1

= \int 32 - sin (x) + 1 d x

Take the constant out:

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

= 32 \cdot \int - sin (x) + 1 d x

Apply u-substitution

: \int \frac{1}{u + 1} d u

= 32 \cdot \int \frac{1}{u + 1} d u

Apply u-substitution

: \int \frac{1}{v} d v

= 32 \cdot \int \frac{1}{v} d v

Simplify

\frac{1}{v} : \frac{1}{v}

= 32 \cdot \int \frac{1}{v} d v

Simplify

= 32 \cdot \int \frac{1}{v} d v

Apply the Power Rule

: 2 v^{\frac{1}{2}}

= 32 \cdot 2 v^{\frac{1}{2}}

Substitute back

= 32 \cdot 2 (sin (x) + 1)^{\frac{1}{2}}

Simplify

32 \cdot 2 (sin (x) + 1)^{\frac{1}{2}} : 62 sin (x) + 1

= 62 sin (x) + 1

Add a constant to the solution

= 62 sin (x) + 1 + C

x \to \infty lim (\frac{1}{x !})

- \frac{1}{x ^{\frac{2}{3}}}

\frac{d}{d x} (sinh^{2} (3 x))

y^{^{''}} + 4 y = 0, y (0) = 4, y^{^{'}} (0) = 1

\int (cos (9 x)) d x

What is the integral of sqrt(18-18sin(x)) ?
The integral of sqrt(18-18sin(x)) is 6sqrt(2)sqrt(sin(x)+1)+C