If `I_n=intxcos^nxdx,prove that: `I_n=1/n cos^(n-1)x(sinx)+(n-1)/(n)I_(n-2)`

Evaluate: If intcos^nxdotdx prove that I_n=1/n(cos^(n-1)xsinx)+((n-1)/n)I_(n-2)

If I_(n)=int cos^(n)x dx . Prove that I_(n)=(1)/(n)(cos^(n-1)x sinx)+((n-1)/(n))I_(n-2) .

If I_(n)=int(sinx+cosx)^(n) dx, snd I_(n)=1/n(sinx+cosx)^(n-1)(sinx-cosx)+(2k)/(n) I_(n-2) then k=

If I_n=int x^nsqrt(a^2-x^2)dx, prove that I_n=-(x^(n-1)(a^2-x^2)^(3/2))/((n+2))+((n+1))/((n+2))a^2I_(n-2)

If I_n=int( lnx)^n dx then I_n+nI_(n-1)

If I_(m,n)= int(sinx)^(m)(cosx)^(n) dx then prove that I_(m,n) = ((sinx)^(m+1)(cosx)^(n-1))/(m+n) +(n-1)/(m+n). I_(m,n-2)

If I_(n)=int_(0)^(pi/2) sin^(n)x dx , then show that I_(n)=((n-1)n)I_(n-2) . Hence prove that I_(n)={(((n-1)/n)((n-3)/(n-2))((n-5)/(n-4))………(1/2)(pi)/2,"if",n"is even"),(((n-1)/n)((n-3)/(n-2))((n-5)/(n-4))………(2/3)1,"if",n"is odd"):}

If I_n=int_0^(pi//4)tan^("n")x dx , prove that I_n+I_(n-2)=1/(n-1)dot

If I_n=intsqrt((a^2+x^2)^n)dx , Prove that: I_n=(xsqrt((a^2+x^2))^n)/(n+1)+(na^2)/(n+1)int(a^2+x^2)^(n/2-1)dx

IfI_n=int_0^1x^n(tan^(-1)x)dx ,t h e np rov et h a t (n+1)I_n+(n-1)I_(n-2)=-1/n+pi/2