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Question
\int \frac{1}{3x^{2}\times 12x^{4}\times 2} dx
Evaluate the integral
-\frac{1}{360x^{5}}+C,C \in \mathbb{R}
Evaluate
\int \frac{1}{3x^{2}\times 12x^{4}\times 2} dx
Multiply
More Steps
Multiply the terms
3x^{2}\times 12x^{4}\times 2
Multiply the terms
More Steps
Evaluate
3\times 12\times 2
Multiply the terms
36\times 2
Multiply the numbers
72
72x^{2}\times x^{4}
Multiply the terms with the same base by adding their exponents
72x^{2+4}
Add the numbers
72x^{6}
\int \frac{1}{72x^{6}} dx
Rewrite the expression
\int \frac{1}{72}\times \frac{1}{x^{6}} dx
\text{Use the property of integral }\int kf(x) dx=k\int f(x) dx
\frac{1}{72}\times \int \frac{1}{x^{6}} dx
\text{Use the property of integral }\int x^{n} dx = \frac{x^{n+1}}{n+1}
\frac{1}{72}\times \frac{x^{-6+1}}{-6+1}
Add the numbers
\frac{1}{72}\times \frac{x^{-5}}{-6+1}
Add the numbers
\frac{1}{72}\times \frac{x^{-5}}{-5}
Divide the terms
More Steps
Evaluate
\frac{x^{-5}}{-5}
\text{Use }\frac{-a}{b}=\frac{a}{-b}=-\frac{a}{b}\text{ to rewrite the fraction}
-\frac{x^{-5}}{5}
\text{Express with a positive exponent using }a^{-n}=\frac{1}{a^n}
-\frac{\frac{1}{x^{5}}}{5}
Simplify
-\frac{1}{5x^{5}}
\frac{1}{72}\left(-\frac{1}{5x^{5}}\right)
Multiplying or dividing an odd number of negative terms equals a negative
-\frac{1}{72}\times \frac{1}{5x^{5}}
Multiply the terms
-\frac{1}{72\times 5x^{5}}
Multiply the terms
-\frac{1}{360x^{5}}
Solution
-\frac{1}{360x^{5}}+C,C \in \mathbb{R}
Show Solutions
