Class 11 Exam > Class 11 Questions > Integrate (2cos x)/(3sin^2 x) dx?
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Integrate (2cos x)/(3sin^2 x) dx?
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Integrate (2cos x)/(3sin^2 x) dx?
Integration of (2cos x)/(3sin^2 x) dx
To integrate (2cos x)/(3sin^2 x) dx, we need to use substitution method and convert the given expression into a form that can be easily integrated.
Step 1: Convert the expression using trigonometric identity.
(2cos x)/(3sin^2 x) = (2cos x)/(3(1-cos^2 x)) = (2/3)(1/(1-cos^2 x)) d(cos x)
Step 2: Substitute u=cos x and du=-sin x dx
(2/3)(1/(1-cos^2 x)) d(cos x) = (2/3)(1/(1-u^2)) d(u) = (2/3) arctan(u) + C
Step 3: Substitute back u=cos x
(2/3) arctan(cos x) + C is the final answer.
Therefore, the integration of (2cos x)/(3sin^2 x) dx is (2/3) arctan(cos x) + C.
To integrate (2cos x)/(3sin^2 x) dx, we need to use substitution method and convert the given expression into a form that can be easily integrated.
Step 1: Convert the expression using trigonometric identity.
(2cos x)/(3sin^2 x) = (2cos x)/(3(1-cos^2 x)) = (2/3)(1/(1-cos^2 x)) d(cos x)
Step 2: Substitute u=cos x and du=-sin x dx
(2/3)(1/(1-cos^2 x)) d(cos x) = (2/3)(1/(1-u^2)) d(u) = (2/3) arctan(u) + C
Step 3: Substitute back u=cos x
(2/3) arctan(cos x) + C is the final answer.
Therefore, the integration of (2cos x)/(3sin^2 x) dx is (2/3) arctan(cos x) + C.
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Integrate (2cos x)/(3sin^2 x) dx?
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Integrate (2cos x)/(3sin^2 x) dx? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Integrate (2cos x)/(3sin^2 x) dx? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Integrate (2cos x)/(3sin^2 x) dx?.
Integrate (2cos x)/(3sin^2 x) dx? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Integrate (2cos x)/(3sin^2 x) dx? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Integrate (2cos x)/(3sin^2 x) dx?.
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