Evaluate :
`int ( u . v )` dx

Evaluate: int dx

Evaluate : int ( cosecx ) dx

Evaluate int logx dx

Evaluate : (i) intx^(9)dx , (ii) int3sqrt(x) dx ,(iii) intdx (iv) int1/(x^(2))dx , (v) int(1)/(x^(1//3))dx , (vi) int5^(x) dx

If u and v are two functions of x then prove that : int uv dx = u int v dx - int [ (du)/(dx) int v dx ] dx Hence, evaluate int x e^(x) dx

Evaluate: int_(0)^(1)|5x-3|dx( ii) int_(0)^( pi)|cos x|dx( iii) int_(-5)^(5)|x-2|dx( iv )int_(-1)^(1)e^(|x|)dx(v)int_(0)^(2)|x^(2)+2x-3|dx(v)int_(1)^(4)(|x-1|+|x-2|+|x-3|)dx( vi) int_(1)^(2)|x^(3)-x|dx

Find the value of int_(u)^(v)Mvdv

If u and v are two functions of x then prove that: int uvdx=u int vdx-int[(du)/(dx)int vdx]dx

Evaluate: a. int_1^2x^3dx , b. int_u^vmvdv c. int_3^4(1/x)dx , d. int_4^9sqrtxdx e. int_0^(pi//4)cos2xdx

int e ^ (- (v) / (u)) dv