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Find the integral of $-\left(5+8f\right)\left(8f-5\right)$

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Solution

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Final answer to the problem

$-\frac{64}{3}f^{3}+25f+C_0$
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Step-by-step Solution

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Find the integral

$\int-\left(5+8f\right)\left(8f-5\right)df$

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$\int-\left(5+8f\right)\left(8f-5\right)df$

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Learn how to solve integral calculus problems step by step online. Find the integral of -(5+8f)(8f-5). Find the integral. The integral of a function times a constant (-1) is equal to the constant times the integral of the function. Rewrite the integrand \left(5+8f\right)\left(8f-5\right) in expanded form. Expand the integral \int\left(64f^2-25\right)df into 2 integrals using the sum rule for integrals, to then solve each integral separately.

Final answer to the problem

$-\frac{64}{3}f^{3}+25f+C_0$

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 -1(5+8f)df using partial fractionsSolve integral of -1(5+8f)df using basic integralsSolve integral of -1(5+8f)df using u-substitutionSolve integral of -1(5+8f)df using integration by partsSolve integral of -1(5+8f)df using trigonometric substitution

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Function Plot

Plotting: $-\frac{64}{3}f^{3}+25f+C_0$

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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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