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

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) (x^(27) cos x + e^x) dx =

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 .

Prove the following int_(0)^(pi/2)sin^(3)xdx=2/3

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 the following: cos^(-1)(4x^(3)-3x)=3cos^(-1)x,x epsilon [1/2,1]

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

Evaluate int_(-1)^(1)sin^(5)xcos^(4)xdx

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