Evaluate `inta^(3x+3)\ dx, agt0`

Evaluate: int_a^b e^-x dx

Evaluate: int_a^b sinx dx as the limit of a sum.

Evaluate int_(0)^(2)(2-3x)^3dx

Evaluate int_(0)^(5)(x^2+3x)dx

Evaluate int_(0)^(3)(x^(3)-6x)dx

Suppose in the definite integral int_a^b f(x) dx the upper limit b->oo, then to obtain the value of int_a^bf(x) dx , we may say that int_a^bf(x)dx=lim_(k->oo)int_a^k dx, where k > a. if f(x)->oo as x ->a or x->b, then the value of definite integral int_a^bf(x)dx is lim_(h->0) int_(a+h)^b f(x) dx. If this limit the value of the limit is defined as the value of integral. This should be noted that f (x)should not have any other discontinuity in [a, b] otherwise this will lead to errorous solution.

Evaluate int_(0)^(1)(2-3x+x^2)dx

What is the value of inta^(x)e^(x)dx ?

Evaluate int_(1)^(a)x.a^(-[log_(e)x])dx,(agt1) .Here [.] represents the greatest integer function.