What is the integral of (10-(14-2sqrt(16-2x))) ?

The integral of (10-(14-2sqrt(16-2x))) is -4x-2/3 (16-2x)^{3/2}+C

Popular >

integral of (10-(14-2sqrt(16-2x)))

\int (10 - (14 - 2 16 - 2 x)) d x

- 4 x - \frac{2}{3} (16 - 2 x)^{\frac{3}{2}} + C

Solution steps

\int 10 - (14 - 2 16 - 2 x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 10 d x - \int 14 - 2 16 - 2 x d x

\int 10 d x = 10 x

\int 14 - 2 16 - 2 x d x = 14 x + \frac{2}{3} (16 - 2 x)^{\frac{3}{2}}

= 10 x - (14 x + \frac{2}{3} (16 - 2 x)^{\frac{3}{2}})

Simplify

= - 4 x - \frac{2}{3} (16 - 2 x)^{\frac{3}{2}}

Add a constant to the solution

= - 4 x - \frac{2}{3} (16 - 2 x)^{\frac{3}{2}} + C

\frac{d}{d x} (\frac{4 - 4 x - x ^{2}}{x ^{2} - 6})

\frac{2 x + 1}{( x ^{2} + 1 ) ^{1.5}}

x \to 0 lim (e^{\frac{1}{x ^{2}}})

x \to 0 - lim (x^{2} - 64)

x \to 0 lim (3 x + 6 x)

What is the integral of (10-(14-2sqrt(16-2x))) ?
The integral of (10-(14-2sqrt(16-2x))) is -4x-2/3 (16-2x)^{3/2}+C