Prove the following
`int_(0)^(1)xe^(x)dx=1`

Prove the following int_(0)^(1)sin^(-1)xdx=pi/2-1

int_(-1)^(1) xe^(x) dx =

Prove the following int_(1)^(3)(dx)/(x^(2)(x+1))=2/3+log2/3

Prove the following int_(-1)^(1)x^(17)cos^(4)xdx=0

Prove that int_(0)^(a) f(x) dx = int_(0)^(a) f(a - x)dx and hence evaluate the following: (d) int_(0)^(1)x(1 -x)^(n)dx .

int_(-1)^(1)(x+1) dx.

Prove that int_(0)^(a) f(x) dx = int_(0)^(a) f(a - x)dx and hence evaluate the following: (f) int_(0)^(pi)(xdx)/(a^(2)cos^(2)x + b^(2)sin^(2)x)

Prove that int_(0)^(a) f(x) dx = int_(0)^(a) f(a - x)dx and hence evaluate the following: (a) int_(0)^(a) (sqrt(x))/(sqrt(x) + sqrt(a) - x)dx

Prove that int_(0)^(a) f(x) dx = int_(0)^(a) f(a - x)dx and hence evaluate the following: (e) int_(0)^(2)xsqrt(2 - x) dx .