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Find the integral $\int\left(4x+2\right)\left(x-1\right)dx$

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Solution

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Final Answer

$\frac{4}{3}x^{3}-x^2-2x+C_0$
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Step-by-step Solution

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1

Rewrite the expression $\left(4x+2\right)\left(x-1\right)$ inside the integral in factored form

$\int2\left(2x+1\right)\left(x-1\right)dx$

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

$\int2\left(2x+1\right)\left(x-1\right)dx$

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Learn how to solve integral calculus problems step by step online. Find the integral int((4x+2)(x-1))dx. Rewrite the expression \left(4x+2\right)\left(x-1\right) inside the integral in factored form. The integral of a function times a constant (2) is equal to the constant times the integral of the function. Rewrite the integrand \left(2x+1\right)\left(x-1\right) in expanded form. Expand the integral \int\left(2x^2-x-1\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately.

Final Answer

$\frac{4}{3}x^{3}-x^2-2x+C_0$

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+2)(x-1)dx using partial fractionsSolve integral of (4x+2)(x-1)dx using basic integralsSolve integral of (4x+2)(x-1)dx using u-substitutionSolve integral of (4x+2)(x-1)dx using integration by partsSolve integral of (4x+2)(x-1)dx using trigonometric substitution

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Function Plot

Plotting: $\frac{4}{3}x^{3}-x^2-2x+C_0$

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5
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7
8
9
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.

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