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Find the integral $\int x\left(5-6x\right)\left(4x^3+5x^2+7\right)^2dx$

Step-by-step Solution

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Solution

Final Answer

$-20x^{8}+\frac{50}{7}x^{7}-28x^{5}-\frac{211}{6}x^{6}+\frac{175}{2}x^{4}+\frac{245}{2}x^2-\frac{32}{3}x^{9}-98x^{3}+C_0$
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Step-by-step Solution

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Rewrite the integrand $x\left(5-6x\right)\left(4x^3+5x^2+7\right)^2$ in expanded form

$\int\left(5x\left(16x^{6}+8x^3\left(5x^2+7\right)+25x^{4}+70x^2+49\right)-6x^2\left(16x^{6}+8x^3\left(5x^2+7\right)+25x^{4}+70x^2+49\right)\right)dx$

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$\int\left(5x\left(16x^{6}+8x^3\left(5x^2+7\right)+25x^{4}+70x^2+49\right)-6x^2\left(16x^{6}+8x^3\left(5x^2+7\right)+25x^{4}+70x^2+49\right)\right)dx$

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Learn how to solve problems step by step online. Find the integral int(x(5-6x)(4x^3+5x^2+7)^2)dx. Rewrite the integrand x\left(5-6x\right)\left(4x^3+5x^2+7\right)^2 in expanded form. Solve the product 5x\left(16x^{6}+8x^3\left(5x^2+7\right)+25x^{4}+70x^2+49\right). Solve the product \left(80x^{6}+5\left(8x^3\left(5x^2+7\right)+25x^{4}+70x^2+49\right)\right)x. Solve the product 5x\left(8x^3\left(5x^2+7\right)+25x^{4}+70x^2+49\right).

Final Answer

$-20x^{8}+\frac{50}{7}x^{7}-28x^{5}-\frac{211}{6}x^{6}+\frac{175}{2}x^{4}+\frac{245}{2}x^2-\frac{32}{3}x^{9}-98x^{3}+C_0$

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 x(5+-6x)dx using partial fractionsSolve integral of x(5+-6x)dx using basic integralsSolve integral of x(5+-6x)dx using u-substitutionSolve integral of x(5+-6x)dx using integration by partsSolve integral of x(5+-6x)dx using trigonometric substitution

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Function Plot

Plotting: $-20x^{8}+\frac{50}{7}x^{7}-28x^{5}-\frac{211}{6}x^{6}+\frac{175}{2}x^{4}+\frac{245}{2}x^2-\frac{32}{3}x^{9}-98x^{3}+C_0$

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a
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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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