`int x/(b+x)dx`

Evaluate: int (x/a +b/x)dx

int (x-b)/(a+x)dx

int(x-a)(x-b)dx=

If f(a+b-x)=f(x) , then int_a^b x f(x)dx is equal to (A) (a-b)/2int_a^b f(a+b-x)dx (B) (a+b)/2int_a^b f(b-x)dx (C) (a+b)/2int_a^b f(x)dx (D) (b-a)/2int_a^b f(x)dx

Evaluate the following integrals : (i) int x^(15)dx (ii) int x^(-3//2)dx (iii) int(3x^(-7)+x^(-1))dx (iv) int(sqrt(x)+(1)/sqrt(x))^(2)dx (v) int(x+(1)/(x))dx (vi) int((a)/(x^(2))+(b)/(x))dx (a and b are constant)

If f(a+b-x)=f(x),\ then prove that \ int_a^b xf(x)dx=(a+b)/2int_a^bf(x)dx

Evaluate int(a^(x))/(b^(x))dx

3. int(cos x)/(a+b sin x)dx

3. int( sin x)/(a+b cos x)dx

int_(a)^(b)sqrt((x-a)/(b-x))dx