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- Indefinite Integral - Basic Integration Rules, Problems, Formulas, Trig Functions, Calculus
Indefinite Integral - Basic Integration Rules, Problems, Formulas, Trig Functions, Calculus
This calculus video tutorial explains how to find the indefinite integral of a function. It explains how to apply basic integration rules and formulas to help you integrate functions.
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Video Transcript
In this video, we're going to go over a
few indefinite integral
problems. So, what is the integral of 4
dx? What is the answer for this problem?
The anti-derivative of a constant, all
you need to do is just add an x to it.
This is going to be 4x. And you also
need to add a a c value. Anytime you
integrate a function, there's always
going to be a constant that you need to
add to it.
Now the derivative of 4x is four. The
derivative of any constant is zero. So
that's why you always need to add the
constant. So what about let's say the
anti-derivative of
pi? Let's say it's dy instead of
dx. All you need to do is add a y
variable to it. It's going to be pi * y
+ c. Now what about the anti-derivative
of e dz?
E is a constant, so it's just going to
be E * Z plus
C. Now, the next type of problem that
you're going to see is when you need to
integrate a variable raised to a
constant. Let's say x raised to the
n. This is equal to x raised to the n +
1 / n + 1 + c.
So for example, let's say if we wish to
find the anti-derivative of x^2
dx. This is equal to x 3r / 3 +
c. The anti-derivative of x
3r is x 4 / 4 +
c. Try this one. What is the
anti-derivative of 8x
cub? So, focus on x^ the 3 power. The 8
is just going to come along for the
ride. The anti-derivative of x 3r is x 4
/ 4. And now we can simplify. 8 / 4 is
2. So the final answer is 2x 4 +
c. Try this one. What is the
anti-derivative of 5x^ 6
power? So using the same technique,
let's add one to the exponent and then
divide by that result. So this is the
answer. Now what about this expression?
What's the anti-derivative of 7x
dx? Well, there is an invisible one. So
we can use the same technique. If we add
