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What is Integration of" 2 log sec x" power of "e" ?
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What is Integration of" 2 log sec x" power of "e" ?
Integration of 2 log(secx)e
Integration is the process of finding the antiderivative of a function. The integration of 2 log(secx)e can be solved by using the substitution method.
Step 1: Use substitution
Let u = sec(x). Therefore, du/dx = sec(x)tan(x)
Using the identity sec2(x) - 1 = tan2(x), we get:
tan2(x) + 1 = sec2(x)
tan2(x) = sec2(x) - 1
tan2(x) = u2 - 1
tan(x)sec(x)dx = du
Step 2: Substitute the value of u and du
The given expression can now be written as:
2 log(u)e sec(x)tan(x)dx
2 log(u)e du
Step 3: Integrate the expression
Now we can integrate the expression:
2 ∫ log(u)e du
Using the power rule of integration:
2 [(u log(u)e) - ∫ u (1/e) du]
2 [(u log(u)e) - (u/e) + C]
Step 4: Substitute the value of u
Substituting the value of u = sec(x), we get:
2 [sec(x) log(sec(x))e - (sec(x)/e) + C]
Final Answer:
The integration of 2 log(secx)e is 2 [sec(x) log(sec(x))e - (sec(x)/e) + C].
Community Answer
What is Integration of" 2 log sec x" power of "e" ?
It can be written as e to the power sec squared x and integration of e to power log sec'2 x will be integration of Sec'2x which is tanx +c
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What is Integration of" 2 log sec x" power of "e" ?
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What is Integration of" 2 log sec x" power of "e" ? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about What is Integration of" 2 log sec x" power of "e" ? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is Integration of" 2 log sec x" power of "e" ?.
What is Integration of" 2 log sec x" power of "e" ? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about What is Integration of" 2 log sec x" power of "e" ? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is Integration of" 2 log sec x" power of "e" ?.
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