Evaluate `intsqrt (2+sin3t) cos3t dt`

Evaluate the following integral: int_0^(pi//4)sin^3 2tcos2t\ dt

int e^(t)(cost-sin t)dt

Find the equation of tangent to the curve given by x=2 sin^(3)t ,y=2 cos^(3)t at a point where t=(pi)/(2) ?

prove: (1) / (2) (cos t + sqrt (3) sin t) = cos ((pi) / (3) -t)

prove: (1) / (2) (cos t + sqrt (3) sin t) = cos ((pi) / (3) -t)

prove: (1) / (2) (cos t + sqrt (3) sin t) = cos ((pi) / (3) -t)

If (1+sin t)(1+cos t)=(5)/(4) then find the value of (1-sin t)(1-cos t)

If (1+sin t)(1+cos t)=(5)/(4) Find the value of (1-sin t)(1-cos t)

Evaluate indefinite integration. (i) x=intdt " " (ii) int t dt " " (iii) x=int (2t) dt" " (iv) x=int (t^(2)) dt " " (v) x=int (-(2)/(t^3))dt