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Integral 2x^12 5x^9/(x^5 x^3 1)^3?
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Integral 2x^12 5x^9/(x^5 x^3 1)^3?
Integration of 2x^12 5x^9/(x^5 x^3 1)^3
Simplifying the denominator
To simplify the denominator, we can combine all the x terms by adding the exponents.
x^5 * x^3 * 1 = x^8
So, we can rewrite the denominator as (x^8)^3 or x^24.
Rewriting the integral
Now, we can rewrite the integral as:
∫ 2x^12 * 5x^9 / x^24 dx
Simplifying the numerator
We can simplify the numerator by adding the exponents of x.
2x^12 * 5x^9 = 10x^21
Rewriting the integral
Now, we can rewrite the integral as:
∫ 10x^21 / x^24 dx
Using the power rule
We can use the power rule of integration to solve this integral.
∫ 10x^21 / x^24 dx = 10 ∫ x^(21-24) dx
= 10 ∫ x^-3 dx
= 10 (-1/2x^2) + C
= -5/x^2 + C
Final answer
Therefore, the final answer is:
∫ 2x^12 5x^9/(x^5 x^3 1)^3 dx = -5/x^2 + C
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Integral 2x^12 5x^9/(x^5 x^3 1)^3?
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Integral 2x^12 5x^9/(x^5 x^3 1)^3? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Integral 2x^12 5x^9/(x^5 x^3 1)^3? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Integral 2x^12 5x^9/(x^5 x^3 1)^3?.
Integral 2x^12 5x^9/(x^5 x^3 1)^3? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Integral 2x^12 5x^9/(x^5 x^3 1)^3? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Integral 2x^12 5x^9/(x^5 x^3 1)^3?.
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