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Integrate $\int\left(\frac{\sqrt[3]{8x}-3x}{x}-2\right)\left(1+\frac{2x-\sqrt[3]{x}}{\sqrt[3]{x}}\right)dx$

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Videos

Implicit differentiation | Advanced derivatives | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=mSVrqKZDRF4

Algebra 2 - Solve for x by combining like terms first, (8x + 1) + (3x - 2) = 32

https://www.youtube.com/watch?v=22iNpGy5vn4

Calculus - Mulitiplying Rational Expressions, ((x^2 - 2x - 3)/(x^2 - 1)) . ((3x - 3)/(x^2 - 4x + 3))

https://www.youtube.com/watch?v=eB9q_okoWFA

Algebra 2 - Simplifying an expression with rational and negative exponents (x^(1/6) y^(1/3))^-18

https://www.youtube.com/watch?v=42cGdWlTRvc

Algebra 2 - When Complex numbers are equal to each other, 5x + 1 + (3 + 2y)i = 2x - 2 + (y - 6)i

https://www.youtube.com/watch?v=avJ0qL4VO6o

Equations with rational expressions | Mathematics III | High School Math | Khan Academy

https://www.youtube.com/watch?v=McOMtxI_Jzs

Function Plot

Plotting: $4x+6\sqrt[3]{x}+\frac{2}{x}-6\sqrt[3]{x^{5}}+C_0$

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a
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d
f
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m
n
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v
w
x
y
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.
(◻)
+
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×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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Main Topic: Implicit Differentiation

Implicit differentiation makes use of the chain rule to differentiate implicitly defined functions. For differentiating an implicit function y(x), defined by an equation R(x, y) = 0, it is not generally possible to solve it explicitly for y(x) and then differentiate. Instead, one can differentiate R(x, y) with respect to x and y and then solve a linear equation in dy/dx for getting explicitly the derivative in terms of x and y.

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