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Integrate the following equation
Let
Integrating by parts, we obtain
Again integrating by parts, we obtain
Integrate the function
Let
Taking x2 as first function and ex as second function and integrating by parts, we obtain
Again integrating by parts, we obtain
Integrate the function
x sin x
Let I =
Taking x as first function and sin x as second function and integrating by parts, we obtain
Integrate the function
Let I =
Taking x as first function and sin 3x as second function and integrating by parts, we obtain
Integrate the function
x logx
Let
Taking log x as first function and x as second function and integrating by parts, we obtain
Integrate the function
x log 2x
Let
Taking log 2x as first function and x as second function and integrating by parts, we obtain
Integrate the function
x2 log x
Let
Taking log x as first function and x2 as second function and integrating by parts, we obtain
Integrate the function
Let
Taking as first function and x as second function and integrating by parts, we obtain
Integrate the function
Let
Taking as first function and x as second function and integrating by parts, we obtain
Integrate the function
Let
Taking cos−1 x as first function and x as second function and integrating by parts, we obtain
Integrate the function
Let
Taking as first function and 1 as second function and integrating by parts, we obtain
Integrate the function
Let
Taking as first function and as second function and integrating by parts, we obtain
Integrate the function
Let
Taking x as first function and sec2x as second function and integrating by parts, we obtain
Integrate the function
Let
Taking as first function and 1 as second function and integrating by parts, we obtain
Integrate the function
Taking as first function and x as second function and integrating by parts, we obtain
Integrate the function
Let
Let I = I1 + I2 … (1)
Where, and
Taking log x as first function and x2 as second function and integrating by parts, we obtain
Taking log x as first function and 1 as second function and integrating by parts, we obtain
Using equations (2) and (3) in (1), we obtain
Integrate the function
Treat the function currently as A * B (A= , B = (sin x + cos x). I am sure, you must be aware how to integrate integral (A*B). Now further for integral B : treat it as integral of C+D , where C = sinx , D = cosx.
First apply basic formula for integral A*B, and dont hurry to replace with actual values. Then solve integral of B as integral of C+D. Once you have values in A, C, D, then only replace.
Let
⇒
∴
It is known that,
Integrate the function
Let
Let ⇒
It is known that,
Integrate the function
Let ⇒
It is known that,
From equation (1), we obtain
Integrate the function
Also, let ⇒
It is known that,
Integrate the function
Let ⇒
It is known that,
Integrate the function
Let ⇒
= 2θ
⇒
Integrating by parts, we obtain
equals
Let
Also, let ⇒
Hence, the correct answer is A.
equals
Let
Also, let ⇒
Hence, the correct answer is A.
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