equals: (A) (B) (C) (D) SOLUTION: Let I = = It is in the form of since here and I = Therefore, The correct option is option (B) .
Choose the correct answer in :
equals to (A) (B) (C) (D) Ans. Let I = = ……….(i) Putting From eq. (i), I = = = Therefore, The correct option is option (B)...
Integrate the functions in-sin^(-1)(2x/1+x^2)
Putting = = = = = = = = = =
Integrate the functions in-e^(2x)sinx
Let I = = I = I = I = = 5I = I =
Integrate the functions in-(x-3)e^x/(x-1)^3
Let I = = = I = It is in the form of since here and = = . I =
Integrate the functions in-e^x(1/x-1/x^2)
Let I = It is in the form of since here and I = =
Integrate the functions in-e^x(1+sinx/1+cosx)
Let I = = = = = It is in the form of since here and =
Integrate the functions in-xe^x/(1+x)^2
Let I = = = I = It is in the form of since here and I =
Integrate the functions in-e^x(sinx+cosx)
Let I = It is in the form of since here and I =
Integrate the functions in-(x^2+1)logx
= = = = = =
Integrate the functions in-x(logx)^2
= = = = = = = =
Integrate the functions in-tan^(-1)x
Let I = = = = = =
Integrate the functions in-xsec^(2)x
= = = = =
Integrate the functions in-xcos^(-1)x/√1-x^2
Let I = ……….(i) Putting I = = = = = = = = =
Integrate the functions in-(sin^(-1)x)^2
Putting = = = = = = =
Integrate the functions in-xcos^(-1)x
Let I = ……….(i) Putting From eq. (i), I = = = = = = = Putting and = =
Integrate the functions in-xtan^(-1)x
Let I = = = = = = = =
Integrate the functions in-xsin^(-1)x
Let I = Putting I = = = = = = = = =
Integrate the functions in- x^2logx
= = = = = =
Integrate the functions in-xlog2x
= = = = = =
Integrate the functions in-xlogx
= = = = = =
Integrate the functions in- x^2e^x
= [Applying product rule] = = = = = = = =
Integrate the functions in- xsin3x
= = = = =
Integrate the functions in – xsinx
= = = = =
Choose the correct answer in each of the following:
equals: (A) (B) (C) (D) SOLUTION: Let I = = = …(i) Putting Putting this value in eq. (i), I = = I = = = = = = Therefore,The correct option is option...
Choose the correct answer in each of the following:
equals: (A) (B) (C) (D) SOLUTION: Let …….(i) = = = Therefore,The correct option is option (B).
Integrate the following function in- 1/(e^x-1)
Let I = …….(i) Putting From eq. (i), I = = = = = = = = = =
Integrate the following function in- 1/x(x^4-1)
Let I = = = …(i) Putting Putting this value in eq. (i), I = = I = = = = = =
Integrate the following function in(x^2+1)(x^2+2)/(x^2+3)(x^2+4)
…….(i) Putting = …….(ii) = ….(iii) Let …….(iv) = = = = =
Integrate the following function in- cosx/(1-sinx)(2-sinx)
Let I = …….(i) Putting From eq. (i), I = = = = = = = = =
Integrate the following function in- $1/x({x^n} + 1)$
Let I = Multiplying both numerator and denominator by , I = = ……..(i) Putting From eq. (i), I = = = = = = = =
Integrate the following function in- 1/(x^4-1)
= Putting , = …..(i) Comparing the coefficients of A + B = 0 ……(ii) Comparing constants A – B = 1 …….(iii) On solving the eq. (ii) and (iii), we get A = B = Putting the values of A, B...
Integrate the following function in- 3x-1/(x+2)^2
Let I = …….(i) Putting Putting this value in eq. (i), I = = = = = = = = =
Integrate the following function in – $2/(1 – x)(1 + {x^2})$
= …….(i) = = = = = = = =
Integrate the following function in
SOLUTION: = …….(i) [On dividing numerator by denominator] Let = = …….(ii) Comparing coefficients of : A + B = 2 …….(iii) Comparing constants: –A + B = 1 …….(iv) On solving eq. (iii) and...
Integrate the following function in
SOLUTION: = = …….(i) Comparing coefficients of : A + +B + C = 0 …….(ii) Comparing coefficients of : –B + 3C= 5 …….(iii) Comparing constants: –4A – 2B + 2C = 0 …….(iv) On solving eq. (i),...
Integrate the following function in
SOLUTION: = = …….(i) Comparing coefficients of : 2A + 2B + C = 0 …….(ii) Comparing coefficients of : 5A + B = 2 …….(iii) Comparing constants: 3A – 3B – C = –3 …….(iv) On solving eq. (i),...
Integrate the following function in
SOLUTION: = = = = = …….(i) Comparing coefficients of : A + C = 0 …….(ii) Comparing coefficients of : B – 2C= 3 …….(iii) Comparing constants: –2A + B + C = 5 …….(iv) On solving eq. (i),...
Integrate the following function in
SOLUTION: = …….(i) Comparing coefficients of : A + C = 0 …….(ii) Comparing coefficients of : A + B – 2C= 1 …….(iii) Comparing constants: –2A + 2B + C = 0 …….(iv) On solving eq. (i), (ii) and...
Integrate the following function in
SOLUTION: …….(i) Comparing coefficients of A + C = 0 …….(ii) Comparing coefficients of , –A + B = 1 …….(iii) Comparing constant terms, –B + C = 0 …….(iv) Solving eq. (ii), (iii) and (iv), we...
Integrate the (rational) function in
SOLUTION: = = = (Dividing numerator by denominator) = …….(i) Now = …….(ii) Comparing coefficients of on both sides –2A + B = …..(iii) Comparing constants A = 1 …….(iv) Solving eq....
Integrate the (rational) function in
SOLUTION: = = = = ….(i) Comparing coefficients of on both sides A + B = 2 …….(ii) Comparing constants 2A + B = 0 …..(iii) Solving eq. (ii) and (iii), we get A = and B = 4 Putting these...
Integrate the (rational) function in
SOLUTION: = …….(i) Comparing coefficients of : A + B + C = 0 …….(ii) Comparing coefficients of : –5A – 4B – 3C= 1 5A + 4B + 3C = –1 …….(iii) Comparing constants: 6A + 3B + 2C = 0 …….(iv) On...
Integrate the (rational) function in
SOLUTION: = …….(i) Comparing coefficients of : A + B + C = 0 …….(ii) Comparing coefficients of : –5A – 4B – 3C= 3 5A + 4B + 3C = –3 …….(iii) Comparing constants: 6A + 3B + 2C = –1 …….(iv) On...
Integrate the (rational) function in
SOLUTION: = = =
Integrate the (rational) function in
SOLUTION: …….(i) Comparing coefficients of on both sides A + B = 1 …..(ii) Comparing constants 2A + B = 0 …..(iii) Solving eq. (ii) and (iii), we get A = and B = 2 Putting these values of A...