∫dxxxn+1 is equal to 

dxxxn+1 is equal to 

  1. A

    logxn+1xn+C

  2. B

    logxnxn+1+C

  3. C

    1nlogxnxn+1+C

  4. D

    nlngxnxn+1+C

    Register to Get Free Mock Test and Study Material

    +91

    Verify OTP Code (required)

    I agree to the terms and conditions and privacy policy.

    Solution:

     Here, partial fractions of given integrand cannot find easily, so we convert it into easy form for partial fractions by multiply xn-1 in both numerator and denominator and then put xn =t. Now, apply partial fractions method and then integrate.

    let  I=1xxn+1dx=xn1xnxn+1dx

    put xn=tnxn1dx=dtxn1dx=1ndt

     I=xn1xnxn+1 dx=1n1t(t+1)dt ----(i)

     Now, 1t(t+1)=At+B(t+1)

     1=A(1+t)+Bt-----ii

    On comparing, we get

    A+B=0,A=1  B=1 I=1n1t1(t+1)dt=1n[log|t|log|t+1|]+C =1nlogtt+1+C=1nlogxnxn+1+C

    Chat on WhatsApp Call Infinity Learn

      Register to Get Free Mock Test and Study Material

      +91

      Verify OTP Code (required)

      I agree to the terms and conditions and privacy policy.