Find the indefinite integral dx x 3 1. Solving indefinite integrals. Introduction to Integrals
Indefinite integral online
At school they say that an integral is the symbol ∫, and the calculation of an integral, that is, the process of integration, is the inverse operation of differentiation. Agree, it's boring!
Of course, schoolchildren have a reasonable question: why do we need him?
But if the teacher had spent a few minutes on an introduction about integrals, such a question would still arise, but not for everyone!
Introduction to Integrals
Back in the 17th century, there were unsolved pressing problems at that time, namely, the patterns of movement of bodies were studied. Newton did a lot of work to understand how the speed of a body is calculated at any given time. But the further it went, the more interesting it turned out to be.
Suppose we know the law of change in the speed of a body - this is a certain function. Then the area of the figure, limited by this curve and the coordinate axis, will be equal to the distance traveled. By calculating the indefinite integral of a function, we find the general law of motion.
This is one of the physical meanings of the integral.
As you already understand, the geometric meaning of the integral is the area of a curvilinear trapezoid. Accordingly, the volume of the body is calculated using a multiple integral.
Solving integrals
Leibniz and Newton laid the foundations of differential and integral calculus. In the following decades there were many great discoveries related to the calculation of integrals.
Since the integrand function can take different forms, this naturally led to the division of integrals into their own types, and most importantly, numerous methods for solving integrals were discovered.
But not everything is so rosy. In practice, it often happens that it is impossible to calculate integrals in analytical form, that is, using any known method. Of course, getting an analytical solution is great, but, on the other hand, the main thing is to calculate the exact value of the integral. In this case, the integrals are solved by numerical methods. Thanks to computer power, such tasks are not particularly difficult for modern people.
Integral solution calculator
Now comes the fun part. Just 15 years ago, a schoolchild could not even imagine that integral calculators such as ours would be at hand. This certainly makes the learning process easier. You can check your decisions, find mistakes and better understand the educational course.
And here we repeat once again, the calculator for solving integrals is just your reliable assistant, which you can turn to at any time. But not a replacement of your head. Try to solve problems on your own, this is the only way to develop your thinking, and the computer will help.
Enter the function for which you need to find the integral
After calculating the indefinite integral, you will be able to receive a free DETAILED solution to the integral you entered.
Let's find the solution to the indefinite integral of the function f(x) (the antiderivative of the function).
Examples
Using degree
(square and cube) and fractions
(x^2 - 1)/(x^3 + 1)
Square root
Sqrt(x)/(x + 1)
Cube root
Cbrt(x)/(3*x + 2)
Using sine and cosine
2*sin(x)*cos(x)
arcsine
X*arcsin(x)
arc cosine
X*arccos(x)
Application of logarithm
X*log(x, 10)
Natural logarithm
Exhibitor
Tg(x)*sin(x)
Cotangent
Ctg(x)*cos(x)
Irrational fractions
(sqrt(x) - 1)/sqrt(x^2 - x - 1)
Arctangent
X*arctg(x)
Arccotangent
X*arсctg(x)
Hyperbolic sine and cosine
2*sh(x)*ch(x)
Hyperbolic tangent and cotangent
Ctgh(x)/tgh(x)
Hyperbolic arcsine and arccosine
X^2*arcsinh(x)*arccosh(x)
Hyberbolic arctangent and arccotangent
X^2*arctgh(x)*arcctgh(x)
Rules for entering expressions and functions
Expressions can consist of functions (notations are given in alphabetical order): absolute(x) Absolute value x
(module x or |x|)
arccos(x) Function - arc cosine of x arccosh(x) Arc cosine hyperbolic from x arcsin(x) Arcsine from x arcsinh(x) Arcsine hyperbolic from x arctan(x) Function - arctangent of x arctgh(x) Arctangent hyperbolic from x e e a number that is approximately equal to 2.7 exp(x) Function - exponent of x(which is e^x)
log(x) or ln(x) Natural logarithm of x
(To get log7(x), you need to enter log(x)/log(7) (or, for example, for log10(x)=log(x)/log(10)) pi The number is "Pi", which is approximately equal to 3.14 sin(x) Function - Sine of x cos(x) Function - Cosine of x sinh(x) Function - Sine hyperbolic from x cosh(x) Function - Cosine hyperbolic from x sqrt(x) Function - square root of x sqr(x) or x^2 Function - Square x tan(x) Function - Tangent from x tgh(x) Function - Tangent hyperbolic from x cbrt(x) Function - cube root of x
The following operations can be used in expressions: Real numbers enter as 7.5
, Not 7,5
2*x- multiplication 3/x- division x^3- exponentiation x+7- addition x - 6- subtraction
Other features: floor(x) Function - rounding x downward (example floor(4.5)==4.0) ceiling(x) Function - rounding x upward (example ceiling(4.5)==5.0) sign(x) Function - Sign x erf(x) Error function (or probability integral) laplace(x) Laplace function
Finding the indefinite integral is a very common problem in higher mathematics and other technical branches of science. Even the simplest physical problems cannot be solved without calculating several simple integrals. Therefore, from school age we are taught techniques and methods for solving integrals; numerous tables are given with integrals of the simplest functions. However, over time, all this is safely forgotten, either we do not have enough time for calculations or we need find the solution to the indefinite integral from a very complex function. To solve these problems, our service will be indispensable for you, allowing you to accurately find indefinite integral online.
Solve indefinite integral
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Even if you want to calculate the integral yourself, thanks to our service it will be easy for you to check your answer, find a mistake or typo, or make sure that the task is completed flawlessly. If you are solving a problem and you need to calculate the indefinite integral as an auxiliary action, then why waste time on these actions that you may have already performed a thousand times? Moreover, additional calculations of the integral may be the cause of a typo or a small error, which subsequently led to an incorrect answer. Just use our services and find indefinite integral online without any effort. For practical problems of finding integral functions online this server is very useful. You need to enter the given function, get online solution of indefinite integral and compare the answer with your solution.