Integral of 587107893/2000x^(-17/5)

\int\frac{587107893}{2000} x^{\left(-\frac{7}{5}\right)}dx

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Answer

$-733884.8663\frac{1}{\sqrt[5]{x^{2}}}+C_0$

Step by step solution

Problem

$\int\frac{587107893}{2000} x^{\left(-\frac{7}{5}\right)}dx$
1

Multiply $-1$ times $\frac{7}{5}$

$\int293553.9465x^{-\frac{7}{5}}dx$
2

Taking the constant out of the integral

$293553.9465\int x^{-\frac{7}{5}}dx$
3

Apply the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a constant function

$293553.9465\left(-\frac{5}{2}\right)x^{-\frac{2}{5}}$
4

Multiply $-\frac{5}{2}$ times $293553.9465$

$-733884.8663x^{-\frac{2}{5}}$
5

Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number

$-733884.8663\frac{1}{\sqrt[5]{x^{2}}}$
6

Apply the formula: $a\frac{1}{x}$$=\frac{a}{x}$, where $a=-733884.8663$ and $x=\sqrt[5]{x^{2}}$

$\frac{-733884.8663}{\sqrt[5]{x^{2}}}$
7

Rewrite the exponent using the power rule $\frac{a^m}{a^n}=a^{m-n}$, where in this case $m=0$

$-733884.8663x^{-\frac{2}{5}}$
8

Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number

$-733884.8663\frac{1}{\sqrt[5]{x^{2}}}$
9

Add the constant of integration

$-733884.8663\frac{1}{\sqrt[5]{x^{2}}}+C_0$

Answer

$-733884.8663\frac{1}{\sqrt[5]{x^{2}}}+C_0$

Problem Analysis

Main topic:

Integral calculus

Time to solve it:

0.24 seconds

Views:

117