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

Step-by-step Solution

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Solution

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Final Answer

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

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We could not solve this problem by using the method: Integrate by substitution

1

Simplify the expression inside the integral

$\int\frac{1}{\sqrt[3]{t^{5}}}dt$

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

$\int\frac{1}{\sqrt[3]{t^{5}}}dt$

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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. Simplify the expression inside the integral. Rewrite the exponent using the power rule \frac{a^m}{a^n}=a^{m-n}, where in this case m=0. Apply the power rule for integration, \displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}, where n represents a number or constant function, such as -\frac{5}{3}. As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration C.

Final Answer

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

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 ((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 integration by partsSolve integral of ((t^2)/(t^(3+8)^0.3333))dt using trigonometric substitution

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Function Plot

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

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a
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n
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x
y
z
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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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Main Topic: Integrals of Rational Functions

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

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