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Integrate $\int\left(x\sqrt{x^2}-10\right)dx$

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Solution

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Final Answer

$\frac{x^{3}}{3}-10x+C_0$
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Step-by-step Solution

Problem to solve:

$\int\left(x\sqrt{x^2}-10\right)dx$

Specify the solving method

1

Simplify the expression inside the integral

$\int x^2dx+\int-10dx$

Learn how to solve integrals with radicals problems step by step online.

$\int x^2dx+\int-10dx$

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Unlock the first 2 steps of this solution.

Learn how to solve integrals with radicals problems step by step online. Integrate int(xx^2^1/2-10)dx. Simplify the expression inside the integral. The integral \int x^2dx results in: \frac{x^{3}}{3}. The integral \int-10dx results in: -10x. Gather the results of all integrals.

Final Answer

$\frac{x^{3}}{3}-10x+C_0$

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 int(xx^2^1/2-10)dx using partial fractionsSolve int(xx^2^1/2-10)dx using basic integralsSolve int(xx^2^1/2-10)dx using u-substitutionSolve int(xx^2^1/2-10)dx using integration by partsSolve int(xx^2^1/2-10)dx using trigonometric substitution

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1
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5
6
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

How to improve your answer:

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Main topic:

Integrals with Radicals

Used formulas:

3. See formulas

Time to solve it:

~ 0.04 s

Related topics:

Integrals with RadicalsCalculusIndefinite Integrals

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