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Find the value of integration dx/x^2(x^4 1)^3/4?
correct answer is-(x^4+1/x^4)^1/4+c?
correct answer is-(x^4+1/x^4)^1/4+c?
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Find the value of integration dx/x^2(x^4 1)^3/4?correct answer is-(x^4...
Integration of dx/x^2(x^4 1)^3/4
To find the value of the given integral, we can use the method of substitution. Let's break down the steps to solve it.
Step 1: Simplify the integral
The given integral can be written as:
∫ dx / (x^2 * (x^4 + 1)^(3/4))
Step 2: Substitute a new variable
Let's substitute a new variable u = x^4 + 1. Taking the derivative of u with respect to x, we have du/dx = 4x^3.
Step 3: Rewrite the integral in terms of the new variable
Using the substitution, we can rewrite the integral as:
∫ (1/4) * (1/u^(3/4)) * (du/4x^3)
Step 4: Simplify the integral further
Simplifying the expression inside the integral, we have:
(1/16) * ∫ (1/u^(3/4)) * (du/x^3)
Step 5: Integrate the new expression
Integrating the simplified expression, we get:
(1/16) * ∫ u^(-3/4) du
Step 6: Evaluate the integral
Integrating u^(-3/4), we have:
(1/16) * (4/1) * u^(1/4) + C
= (1/4) * u^(1/4) + C
= (1/4) * (x^4 + 1)^(1/4) + C
Therefore, the value of the given integral is:
(1/4) * (x^4 + 1)^(1/4) + C, where C is the constant of integration.
To find the value of the given integral, we can use the method of substitution. Let's break down the steps to solve it.
Step 1: Simplify the integral
The given integral can be written as:
∫ dx / (x^2 * (x^4 + 1)^(3/4))
Step 2: Substitute a new variable
Let's substitute a new variable u = x^4 + 1. Taking the derivative of u with respect to x, we have du/dx = 4x^3.
Step 3: Rewrite the integral in terms of the new variable
Using the substitution, we can rewrite the integral as:
∫ (1/4) * (1/u^(3/4)) * (du/4x^3)
Step 4: Simplify the integral further
Simplifying the expression inside the integral, we have:
(1/16) * ∫ (1/u^(3/4)) * (du/x^3)
Step 5: Integrate the new expression
Integrating the simplified expression, we get:
(1/16) * ∫ u^(-3/4) du
Step 6: Evaluate the integral
Integrating u^(-3/4), we have:
(1/16) * (4/1) * u^(1/4) + C
= (1/4) * u^(1/4) + C
= (1/4) * (x^4 + 1)^(1/4) + C
Therefore, the value of the given integral is:
(1/4) * (x^4 + 1)^(1/4) + C, where C is the constant of integration.
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Find the value of integration dx/x^2(x^4 1)^3/4?correct answer is-(x^4+1/x^4)^1/4+c?
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Find the value of integration dx/x^2(x^4 1)^3/4?correct answer is-(x^4+1/x^4)^1/4+c? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Find the value of integration dx/x^2(x^4 1)^3/4?correct answer is-(x^4+1/x^4)^1/4+c? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the value of integration dx/x^2(x^4 1)^3/4?correct answer is-(x^4+1/x^4)^1/4+c?.
Find the value of integration dx/x^2(x^4 1)^3/4?correct answer is-(x^4+1/x^4)^1/4+c? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Find the value of integration dx/x^2(x^4 1)^3/4?correct answer is-(x^4+1/x^4)^1/4+c? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the value of integration dx/x^2(x^4 1)^3/4?correct answer is-(x^4+1/x^4)^1/4+c?.
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