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Find the integral $\int\frac{1}{\sqrt[5]{x^7}}dx$

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Solution

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Final Answer

$-\frac{5}{2}x^{-\frac{2}{5}}+C_0$
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Step-by-step Solution

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Simplify $\sqrt[5]{x^7}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $7$ and $n$ equals $\frac{1}{5}$

$\int\frac{1}{\sqrt[5]{x^{7}}}dx$

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

$\int\frac{1}{\sqrt[5]{x^{7}}}dx$

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Learn how to solve integrals of rational functions problems step by step online. Find the integral int(1/(x^7^1/5))dx. Simplify \sqrt[5]{x^7} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 7 and n equals \frac{1}{5}. 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{7}{5}. Divide 1 by -\frac{2}{5}.

Final Answer

$-\frac{5}{2}x^{-\frac{2}{5}}+C_0$

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/(x^7^0.2))dx using partial fractionsSolve integral of (1/(x^7^0.2))dx using basic integralsSolve integral of (1/(x^7^0.2))dx using u-substitutionSolve integral of (1/(x^7^0.2))dx using integration by partsSolve integral of (1/(x^7^0.2))dx using trigonometric substitution

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Plotting: $-\frac{5}{2}x^{-\frac{2}{5}}+C_0$

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0
a
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n
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x
y
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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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