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Find the integral of $\left(2x^3-8x\right)\left(6x+6\right)-\left(3x^2+6x\right)\left(6x^2-8\right)$

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Solution

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Final Answer

$-\frac{6}{5}x^{5}-6x^{4}-8x^{3}+C_0$
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Step-by-step Solution

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Find the integral

$\int\left(\left(2x^3-8x\right)\left(6x+6\right)-\left(3x^2+6x\right)\left(6x^2-8\right)\right)dx$

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$\int\left(\left(2x^3-8x\right)\left(6x+6\right)-\left(3x^2+6x\right)\left(6x^2-8\right)\right)dx$

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Learn how to solve integral calculus problems step by step online. Find the integral of (2x^3-8x)(6x+6)-(3x^2+6x)(6x^2-8). Find the integral. Multiply the single term 6x+6 by each term of the polynomial \left(2x^3-8x\right). Solve the product 2x^3\left(6x+6\right). Multiply the single term x^3 by each term of the polynomial \left(12x+12\right).

Final Answer

$-\frac{6}{5}x^{5}-6x^{4}-8x^{3}+C_0$

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 ((2x^3+-8x)(6x+6)+-1(3x^2+6x))dx using partial fractionsSolve integral of ((2x^3+-8x)(6x+6)+-1(3x^2+6x))dx using basic integralsSolve integral of ((2x^3+-8x)(6x+6)+-1(3x^2+6x))dx using u-substitutionSolve integral of ((2x^3+-8x)(6x+6)+-1(3x^2+6x))dx using integration by partsSolve integral of ((2x^3+-8x)(6x+6)+-1(3x^2+6x))dx using trigonometric substitution

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Plotting: $-\frac{6}{5}x^{5}-6x^{4}-8x^{3}+C_0$

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x
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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: 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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