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Integrate the function $\frac{4x^3-12x^2-2x+10}{\frac{7}{2}x^2-7x-\frac{6}{4}}$

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Solution

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Final answer to the problem

$-\frac{4}{21}x^{3}+\frac{45}{49}x^2-\frac{37}{343}x+1.1758889\ln\left(x-2.1952286\right)-1.1758889\ln\left(x+\frac{41}{210}\right)+C_0$
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Step-by-step Solution

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Find the integral

$\int\frac{4x^3-12x^2-2x+10}{\frac{7}{2}x^2-7x-\frac{6}{4}}dx$

Learn how to solve integral calculus problems step by step online.

$\int\frac{4x^3-12x^2-2x+10}{\frac{7}{2}x^2-7x-\frac{6}{4}}dx$

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Learn how to solve integral calculus problems step by step online. Integrate the function (4x^3-12x^2-2x+10)/(7/2x^2-7x-6/4). Find the integral. Simplifying. Divide 4x^3-12x^2-2x+10 by \frac{7}{2}x^2-7x-\frac{3}{2}. Resulting polynomial.

Final answer to the problem

$-\frac{4}{21}x^{3}+\frac{45}{49}x^2-\frac{37}{343}x+1.1758889\ln\left(x-2.1952286\right)-1.1758889\ln\left(x+\frac{41}{210}\right)+C_0$

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve integral of ((4x^3+-12x^2)/(7/2x^2+-7x))dx using partial fractionsSolve integral of ((4x^3+-12x^2)/(7/2x^2+-7x))dx using basic integralsSolve integral of ((4x^3+-12x^2)/(7/2x^2+-7x))dx using u-substitutionIntegrate using trigonometric identitiesSolve integral of ((4x^3+-12x^2)/(7/2x^2+-7x))dx using trigonometric substitution

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Function Plot

Plotting: $-\frac{4}{21}x^{3}+\frac{45}{49}x^2-\frac{37}{343}x+1.1758889\ln\left(x-2.1952286\right)-1.1758889\ln\left(x+\frac{41}{210}\right)+C_0$

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0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻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: Integral Calculus

Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

Used Formulas

See formulas (7)

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