Evaluate the integral: \[ \int \frac{dx}{4 + 3\cot x} \]
Evaluate the integral: \[ \int \frac{dx}{(x+1)\sqrt{x^2 + 4}} \]
If \[ \int e^x (x^3 + x^2 - x + 4) \, dx = e^x f(x) + C, \] then \( f(1) \) is:
Evaluate the integral: \[ \int_{\frac{\pi}{5}}^{\frac{3\pi}{10}} \frac{dx}{\sec^2 x + (\tan^{2022} x - 1)(\sec^2 x - 1)} \]
Let y = t2 - 4t -10 and ax + by + c = 0 be the equation of the normal L. If G.C.D of (a,b,c) is 1, then m(a+b+c) =
If the function f(x) = xe -x , x ∈ R attains its maximum value β at x = α then (α, β) =
\(\int_{\frac{-\pi}{2}}^{\frac{\pi}{2}} sin^2xcos^2x(sinx+cosx)dx=\)
The area (in square units) of the region bounded by the curve y = |sin2x| and the X-axis in [0,2π] is
If \(\int_{0}^{3} (3x^2-4x+2) \,dx = k,\) then an integer root of 3x2-4x+2= \(\frac{3k}{5}\) is