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

Step-by-step Solution

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Final Answer

$\frac{1}{3}x^{6}+\frac{-x^{8}}{8}+C_0$
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Step-by-step Solution

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When multiplying exponents with same base you can add the exponents: $x\left(2-x^2\right)x^4$

$\int x^{5}\left(2-x^2\right)dx$

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$\int x^{5}\left(2-x^2\right)dx$

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Learn how to solve integral calculus problems step by step online. Find the integral int(x(2-x^2)x^4)dx. When multiplying exponents with same base you can add the exponents: x\left(2-x^2\right)x^4. Rewrite the integrand x^{5}\left(2-x^2\right) in expanded form. Expand the integral \int\left(2x^{5}-x^{7}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int2x^{5}dx results in: \frac{1}{3}x^{6}.

Final Answer

$\frac{1}{3}x^{6}+\frac{-x^{8}}{8}+C_0$

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

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Plotting: $\frac{1}{3}x^{6}+\frac{-x^{8}}{8}+C_0$

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1
2
3
4
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
Dx
|◻|
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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