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Find the integral $\int\frac{t^2}{\sqrt[3]{t^{\left(3+8\right)}}}dt$

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Solution

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Final Answer

$\frac{-3}{2\sqrt[3]{t^{2}}}+C_0$
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Step-by-step Solution

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Rewrite the fraction $\frac{t^2}{\sqrt[3]{t^{\left(3+8\right)}}}$ inside the integral as the product of two functions: $t^2\frac{1}{\sqrt[3]{t^{\left(3+8\right)}}}$

$\int t^2\frac{1}{\sqrt[3]{t^{\left(3+8\right)}}}dt$

Learn how to solve integrals of rational functions problems step by step online.

$\int t^2\frac{1}{\sqrt[3]{t^{\left(3+8\right)}}}dt$

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Learn how to solve integrals of rational functions problems step by step online. Find the integral int((t^2)/(t^(3+8)^1/3))dt. Rewrite the fraction \frac{t^2}{\sqrt[3]{t^{\left(3+8\right)}}} inside the integral as the product of two functions: t^2\frac{1}{\sqrt[3]{t^{\left(3+8\right)}}}. We can solve the integral \int t^2\frac{1}{\sqrt[3]{t^{\left(3+8\right)}}}dt by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify u and calculate du. Now, identify dv and calculate v.

Final Answer

$\frac{-3}{2\sqrt[3]{t^{2}}}+C_0$

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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 ((t^2)/(t^(3+8)^0.3333))dt using partial fractionsSolve integral of ((t^2)/(t^(3+8)^0.3333))dt using basic integralsSolve integral of ((t^2)/(t^(3+8)^0.3333))dt using u-substitutionSolve integral of ((t^2)/(t^(3+8)^0.3333))dt using trigonometric substitution

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Function Plot

Plotting: $\frac{-3}{2\sqrt[3]{t^{2}}}+C_0$

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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: Integrals of Rational Functions

Integrals of rational functions of the form R(x) = P(x)/Q(x).

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