`int_1^2 2pi x(2-x) dx`

int_1^pi 1/(1+x^2) dx

int_0^(pi/2) (x^2+x)dx

Evaluate: int_1^2 1/((x+1)(x+2))dx (ii) int_1^2 1/(x(1+x^2))dx

IfI_1=int_0^1 2^(x^2)dx ,I_2=int_0^1 2^(x^3)dx ,I_3=int_1^2 2^(x^2)dx ,I_4=int_1^2 2^(x^3)dx , then which of the following is/are true?

Evaluate: (i) int1/(a^2-b^2\ x^2)\ dx (ii) int1/(a^2\ x^2-b^2)\ dx

Evaluate: (i) int1/(a^2-b^2\ x^2)\ dx (ii) int1/(a^2\ x^2-b^2)\ dx

Evaluate int_0^pi x/(a^2-cos^2x)dx

If A=int_0^pi cosx/(x+2)^2 \ dx , then int_0^(pi//2) (sin 2x)/(x+1) \ dx is equal to

1) int_(-pi/2)^pi sin^(-1) (sinx) dx 2) int_(-pi/2)^(pi/2) (-pi/2)/(sqrt(cos x sin^2 x)) dx 3) int_0^2 2x[x] dx

int_0^1(tan^(-1)x)/x dx is equals to (a) int_0^(pi/2)(sinx)/x dx (b) int_0^(pi/2)x/(sinx)dx (c) 1/2int_0^(pi/2)(sinx)/x dx (d) 1/2int_0^(pi/2)(""x)/(sinx)dx