Evaluate the following`int_(0)^(oo)x^(5)e^(-3x)dx`

1. int_(0)^(oo)e^(-x/2)dx

Evaluate the following: (i) int(sec^(2)x)/(3+tanx)dx " (ii) " int(e^(x)-e^(-x))/(e^(x)+e^(-x))dx (iii) int(1-tanx)/(1+tanx)dx " (iv) " int(1)/(1+e^(-x))dx

int_(0)^(1)e^(2x)e^(e^(x) dx =)

Evaluate the following integrals (i) int_(R)^(oo)(GMm)/(x^(2))dx (ii) int_(r_(1))^(r_(2)) -k(q_1q_2)/(x^(2))dx (iii) int_(u)^(v) Mv dv (iv) int_(0)^(oo) x^(-1//2) dx (v) int_(0)^(pi//2) sinx dx (vi) int_(0)^(pi//2) cosx dx (vii) int_(-pi//2)^(pi//2) cos x dx

Evaluate the following integrals: int_-5^0f(x)dx ,w h e r ef(x)=|x|+|x+2|+|x+5|

Evaluate the following integral: int_0^1(e^x)/(1+e^(2x))dx

Evaluate the following integral: int_0^oo(logx)/(1+x^2)dx

Evaluate : int_(0)^(oo)(cot^(-1)x)^(2)dx

Evaluate the following integral: int_0^3|3x-1|dx

Evaluate the following integrals : int_0^(3.)(2x^2+3x+5)dx