Was solving a problem in mathematics and came across the following integration. Unable to move further. Can somebody provide answer for the following ( a and b are constants ).
A good plan to tackle such questions is: remove what disturbs the most! That often helps to get into the problem. If you have trig functions then it is always good to keep the Weierstraß substitution in mind; not here but in general.
On its own, just as a trick, ##sinxcosx=\frac{sin2x}{2}##, with simple integral ##\frac{-Cos2x}{2}##
But, yes, that denominator kills it. Maybe Fresh can write an insight on integrating expressions a/b from the respective integrals of a,b , right, Fresh? ;)
On its own, just as a trick, ##sinxcosx=\frac{sin2x}{2}##, with simple integral ##\frac{-Cos2x}{2}##
But, yes, that denominator kills it. Maybe Fresh can write an insight on integrating expressions a/b from the respective integrals of a,b , right, Fresh? ;)
The difficulty with integrating products (and likewise quotients) arises from the fact that differentiation is a derivation. The Jacobi identity / Leibniz rule / product rule rules this world and not the chain rule.
$$
D(f\cdot g) = Df \cdot g + f\cdot Dg
$$
We can sometimes use the fact the ##D\sin= \cos## and ##D\cos= -\sin## and in the case of trigonometric functions. Here is an example: https://www.physicsforums.com/insig...tion/#Integration-by-Parts-–-The-Leibniz-Rule
