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Indefinite Integral of (1-√x/1 ⁴√x)dx?
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Indefinite Integral of (1-√x/1 ⁴√x)dx?
Integration of (1+√x)/(1-x^1/4)
integration of {(1+x^1/4)(1-x^1/4)}/(1+x^1/4)
using, a^2-b^2=(a+b)(a-b)
integration of (1-x^1/4)dx =x-(4x^5/4)/5+K
integration of {(1+x^1/4)(1-x^1/4)}/(1+x^1/4)
using, a^2-b^2=(a+b)(a-b)
integration of (1-x^1/4)dx =x-(4x^5/4)/5+K
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Indefinite Integral of (1-√x/1 ⁴√x)dx?
Indefinite Integral of (1-√x/1 ⁴√x)dx
To evaluate the indefinite integral of (1-√x/1 ⁴√x)dx, we need to use the substitution method. Let u = √x, then du/dx = 1/2√x, and dx = 2u du. We can rewrite the integral as follows:
∫ (1-√x/1 ⁴√x)dx = ∫ (1-u/u⁴)2udu
Split the Integral
We can split the integral into two parts:
∫ (1-u)2/u⁴ du - ∫ u2/u⁴ du
Simplify the Integral
Simplifying, we get:
∫ (1-2u+u²)/u⁴ du - ∫ u⁻² du
∫ (u⁻⁴ - 2u⁻³ + u⁻²) du - ∫ u⁻² du
- u⁻³ + u⁻¹ + C - u⁻¹ + C'
Substitute original value
Substituting back u = √x, we get:
- 1/√x + 1/x + C - 1/x + C'
Simplifying, we get:
- 1/√x + C
Therefore, the indefinite integral of (1-√x/1 ⁴√x)dx is - 1/√x + C.
To evaluate the indefinite integral of (1-√x/1 ⁴√x)dx, we need to use the substitution method. Let u = √x, then du/dx = 1/2√x, and dx = 2u du. We can rewrite the integral as follows:
∫ (1-√x/1 ⁴√x)dx = ∫ (1-u/u⁴)2udu
Split the Integral
We can split the integral into two parts:
∫ (1-u)2/u⁴ du - ∫ u2/u⁴ du
Simplify the Integral
Simplifying, we get:
∫ (1-2u+u²)/u⁴ du - ∫ u⁻² du
∫ (u⁻⁴ - 2u⁻³ + u⁻²) du - ∫ u⁻² du
- u⁻³ + u⁻¹ + C - u⁻¹ + C'
Substitute original value
Substituting back u = √x, we get:
- 1/√x + 1/x + C - 1/x + C'
Simplifying, we get:
- 1/√x + C
Therefore, the indefinite integral of (1-√x/1 ⁴√x)dx is - 1/√x + C.
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Indefinite Integral of (1-√x/1 ⁴√x)dx?
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Indefinite Integral of (1-√x/1 ⁴√x)dx? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Indefinite Integral of (1-√x/1 ⁴√x)dx? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Indefinite Integral of (1-√x/1 ⁴√x)dx?.
Indefinite Integral of (1-√x/1 ⁴√x)dx? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Indefinite Integral of (1-√x/1 ⁴√x)dx? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Indefinite Integral of (1-√x/1 ⁴√x)dx?.
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