Integrate (x(x(2x^(2+1))/*s^4*c)^0.5*n^3*s)^0.5

\int\sqrt{s\cdot n3\cdot x\sqrt{c\cdot s4\cdot x\cdot\frac{2x^{\left(2+1\right)}}{}}}dx

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Answer

$\frac{1}{\sqrt[4]{}}\int\frac{\sqrt[3]{31}}{2}s\sqrt{n^{3}}\sqrt{s}\sqrt[4]{c}\sqrt{x^{3}}dx$

Step by step solution

Problem

$\int\sqrt{s\cdot n3\cdot x\sqrt{c\cdot s4\cdot x\cdot\frac{2x^{\left(2+1\right)}}{}}}dx$
1

Add the values $2$ and $1$

$\int\sqrt{x\cdot s\sqrt{x\cdot c\frac{2x^{3}}{}s^4}n^3}dx$
2

The power of a product is equal to the product of it's factors raised to the same power

$\int s\sqrt[4]{\frac{2x^{3}}{}}\sqrt{x}\sqrt[4]{x}\sqrt{n^{3}}\sqrt{s}\sqrt[4]{c}dx$
3

The power of a quotient is equal to the quotient of the power of the numerator and denominator: $\displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}$

$\int s\frac{\sqrt[4]{2x^{3}}}{\sqrt[4]{}}\sqrt{x}\sqrt[4]{x}\sqrt{n^{3}}\sqrt{s}\sqrt[4]{c}dx$
4

When multiplying exponents with same base we can add the exponents

$\int s\frac{\sqrt[4]{2x^{3}}}{\sqrt[4]{}}\sqrt{n^{3}}\sqrt{s}\sqrt[4]{c}\sqrt[4]{x^{3}}dx$
5

The power of a product is equal to the product of it's factors raised to the same power

$\int s\frac{\frac{\sqrt[3]{31}}{2}\sqrt[4]{x^{3}}}{\sqrt[4]{}}\sqrt{n^{3}}\sqrt{s}\sqrt[4]{c}\sqrt[4]{x^{3}}dx$
6

Multiplying the fraction and term

$\int\frac{\frac{\sqrt[3]{31}}{2}s\sqrt[4]{x^{3}}\sqrt{n^{3}}\sqrt{s}\sqrt[4]{c}\sqrt[4]{x^{3}}}{\sqrt[4]{}}dx$
7

When multiplying exponents with same base you can add the exponents

$\int\frac{\frac{\sqrt[3]{31}}{2}s\sqrt{n^{3}}\sqrt{s}\sqrt[4]{c}\left(\sqrt[4]{x^{3}}\right)^2}{\sqrt[4]{}}dx$
8

Applying the power of a power property

$\int\frac{\frac{\sqrt[3]{31}}{2}s\sqrt{n^{3}}\sqrt{s}\sqrt[4]{c}\sqrt{x^{3}}}{\sqrt[4]{}}dx$
9

Taking the constant out of the integral

$\frac{1}{\sqrt[4]{}}\int\frac{\sqrt[3]{31}}{2}s\sqrt{n^{3}}\sqrt{s}\sqrt[4]{c}\sqrt{x^{3}}dx$
10

Multiplying the fraction and term

$\frac{\int\frac{\sqrt[3]{31}}{2}s\sqrt{n^{3}}\sqrt{s}\sqrt[4]{c}\sqrt{x^{3}}dx}{\sqrt[4]{}}$
11

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

$^{-\frac{1}{4}}\int\frac{\sqrt[3]{31}}{2}s\sqrt{n^{3}}\sqrt{s}\sqrt[4]{c}\sqrt{x^{3}}dx$
12

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

$\frac{1}{\sqrt[4]{}}\int\frac{\sqrt[3]{31}}{2}s\sqrt{n^{3}}\sqrt{s}\sqrt[4]{c}\sqrt{x^{3}}dx$

Answer

$\frac{1}{\sqrt[4]{}}\int\frac{\sqrt[3]{31}}{2}s\sqrt{n^{3}}\sqrt{s}\sqrt[4]{c}\sqrt{x^{3}}dx$

Problem Analysis

Main topic:

Integral calculus

Time to solve it:

0.36 seconds

Views:

94