What is the integral of (8-128x)/(sqrt(49-64x^2)) ?

The integral of (8-128x)/(sqrt(49-64x^2)) is 2sqrt(-64x^2+49)+arcsin(8/7 x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (8-128x)/(sqrt(49-64x^2))

\int \frac{8 - 128 x}{49 - 64 x ^{2}} d x

2 - 64 x^{2} + 49 + arcsin (\frac{8}{7} x) + C

Solution steps

\int \frac{8 - 128 x}{49 - 64 x ^{2}} d x

Apply Trigonometric Substitution

: \int - 14 sin (u) + 1 d u

= \int - 14 sin (u) + 1 d u

Apply the Sum Rule:

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

= - \int 14 sin (u) d u + \int 1 d u

\int 14 sin (u) d u = - 14 cos (u)

\int 1 d u = u

= - (- 14 cos (u)) + u

Substitute back

u = arcsin (\frac{8}{7} x)

= - (- 14 cos (arcsin (\frac{8}{7} x))) + arcsin (\frac{8}{7} x)

Simplify

- (- 14 cos (arcsin (\frac{8}{7} x))) + arcsin (\frac{8}{7} x) : 2 - 64 x^{2} + 49 + arcsin (\frac{8}{7} x)

= 2 - 64 x^{2} + 49 + arcsin (\frac{8}{7} x)

Add a constant to the solution

= 2 - 64 x^{2} + 49 + arcsin (\frac{8}{7} x) + C

\frac{\partial}{\partial x} (3 x^{3} + 4 x^{2} y - 3 y^{3})

x \to 0 lim (\frac{3 8 + x - 3 8}{x})

\int \frac{x + 5}{x ^{2} + 10 x + 26} d x

\frac{d y}{d t} = 3 t^{2} cos (t^{3})

x^{- x}

What is the integral of (8-128x)/(sqrt(49-64x^2)) ?
The integral of (8-128x)/(sqrt(49-64x^2)) is 2sqrt(-64x^2+49)+arcsin(8/7 x)+C