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To solve this, we must use integration by parts as we can’t solve it directly. The formula for integration by parts is integral(U dV)=U V-integral(V*dU). The trick with this is to set dV=1 and to set U=ln(x)...

Make use of identity sech^2(x) = tan^2(x) + 1 => 2{tan^2(x) + 1} = 3 + tan(x) Multiply out brackets and rearrange => 2tan^2(x) - tan(x) - 1 = 0 Use quadratic formula with a = 2, b = -1, c = -1 => ta...

If you have a differentiable function, stationary points are, by definition, those points where the derivative of the function is 0. Considering that the derivative of a function represents the rate of incre...

∫(8x3 + 4) dx = (8x^4)/4 + 4x + c= 2x^4 + 4x + c

We know that tan x =sin x/cos x, so we can multiply the whole equation by cos x which gives us => 2cos^2 x =3 sin x from the trig identity sin^2 (x)+ cos^2 (x)=1, we can sub in cos^2 (x)=1-sin^2(x) => ...