ihow use shortcuts for integral calculus

Hello student,
First of all, in order to excel in integral calculus the inetgration formulae should be on your finger tips. There is no shortcut to hardwork and practice, but yes, there are some shortcuts that you can apply in order to reach the solution quickly and easily.
1. In case of composition of functions, you can follow the following steps:
(a) Write down the reciprocal of the coefficient of x.
(b) Write down the inner function and multiply it by the integral of the outer function as you would do in case of Chain rule in differentiation.
(c) Add C.
Eg: ∫ sec²7x
Now, this is infact (sec 7x)², so the outer function is sec²x and the inner function is 7x.
So, write down the reciprocal of inner function and multiply it by integral of outer.
1/7. tan 7x
Now, just add C.
= 1/7 . tan 7x + C.
2. In case of area bounded by curves, follow the below listed steps:
(a) Draw the graph.
(b) Find the points of intersection.
(c) Calculate area below top curve.
(d) Calculate area below bottom curve.
(e) Subtract (d) from (c).
For more methods, you can visit the website and the section of integral calculus