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Integrate 6x + 5 x^2 - 2 x^3 + 1 /x?
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Integrate 6x + 5 x^2 - 2 x^3 + 1 /x?
Integration of 6x + 5x^2 - 2x^3 + 1/x
To integrate the given function, we will follow the rules of integration for each term separately.
Integration of 6x:
The integral of 6x with respect to x is 3x^2 + C, where C is the constant of integration.
Integration of 5x^2:
The integral of 5x^2 with respect to x is (5/3)x^3 + C.
Integration of -2x^3:
The integral of -2x^3 with respect to x is (-1/2)x^4 + C.
Integration of 1/x:
The integral of 1/x with respect to x is ln |x| + C.
Combining all the integrals:
Putting all the integrals together, we get the final result:
3x^2 + (5/3)x^3 - (1/2)x^4 + ln |x| + C
Therefore, the integration of 6x + 5x^2 - 2x^3 + 1/x with respect to x is 3x^2 + (5/3)x^3 - (1/2)x^4 + ln |x| + C, where C is the constant of integration.
To integrate the given function, we will follow the rules of integration for each term separately.
Integration of 6x:
The integral of 6x with respect to x is 3x^2 + C, where C is the constant of integration.
Integration of 5x^2:
The integral of 5x^2 with respect to x is (5/3)x^3 + C.
Integration of -2x^3:
The integral of -2x^3 with respect to x is (-1/2)x^4 + C.
Integration of 1/x:
The integral of 1/x with respect to x is ln |x| + C.
Combining all the integrals:
Putting all the integrals together, we get the final result:
3x^2 + (5/3)x^3 - (1/2)x^4 + ln |x| + C
Therefore, the integration of 6x + 5x^2 - 2x^3 + 1/x with respect to x is 3x^2 + (5/3)x^3 - (1/2)x^4 + ln |x| + C, where C is the constant of integration.
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Integrate 6x + 5 x^2 - 2 x^3 + 1 /x?
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Integrate 6x + 5 x^2 - 2 x^3 + 1 /x? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Integrate 6x + 5 x^2 - 2 x^3 + 1 /x? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Integrate 6x + 5 x^2 - 2 x^3 + 1 /x?.
Integrate 6x + 5 x^2 - 2 x^3 + 1 /x? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Integrate 6x + 5 x^2 - 2 x^3 + 1 /x? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Integrate 6x + 5 x^2 - 2 x^3 + 1 /x?.
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