The indefinite integral 3 x 2 dx is equal. Solving the integral online. Introduction to integrals
Enter the function for which you want to find the integral
After calculating the indefinite integral, you can get free DETAILED solution the integral you entered.
Let's find the solution of the indefinite integral of the function f(x) (the antiderivative of the function).
Examples
With the use of 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 the 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)
Arc tangent
X*arсctg(x)
Hyberbolic sine and cosine
2*sh(x)*ch(x)
Hyberbolic tangent and cotangent
ctgh(x)/tgh(x)
Hyberbolic arcsine and arccosine
X^2*arcsinh(x)*arccosh(x)
Hyberbolic arctangent and arccotangent
X^2*arctgh(x)*arctgh(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 arctg(x) Function - arc tangent from x arctgh(x) The arc tangent is hyperbolic from x e e a number that is approximately equal to 2.7 exp(x) Function - exponent from x(which is e^x)
log(x) or log(x) Natural logarithm of x
(To obtain 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 - Hyperbolic sine of x cash(x) Function - Hyperbolic cosine of x sqrt(x) The function is the square root of x sqr(x) or x^2 Function - Square x tg(x) Function - Tangent from x tgh(x) Function - Hyperbolic tangent of x cbrt(x) The function is the cube root of x
You can use the following operations in expressions: Real numbers enter in the form 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 down (example floor(4.5)==4.0) ceiling(x) Function - rounding x up (example ceiling(4.5)==5.0) sign(x) Function - Sign x erf(x) Error function (or probability integral) laplace(x) Laplace function
Indefinite integral online
At school they say that the integral is the symbol ∫, and the calculation of the integral, that is, the process of integration, is the operation inverse to differentiation. Agree boring!
Of course, students have a reasonable question: and what the heck do we need?
But if the teacher had spent a few minutes on the introductory about integrals, such a question would still have arisen, but not for everyone!
Introduction to integrals
Back in the 17th century, there were unresolved pressing problems at that time, namely, the laws of motion of bodies were studied. A lot of work was done by Newton to understand how the speed of a body is calculated at any given time. But the further, the more interesting it turned out.
Suppose we know the law of change in the speed of the body - this is a certain function. Then the area of the figure bounded by this curve and the coordinate axis will be equal to the distance traveled. Calculating the indefinite integral of the function, we just find the general law of motion.
This is one of the physical meanings of the integral.
As you already understood, the geometric meaning of the integral is the area of a curvilinear trapezoid. Accordingly, using the multiple integral, the volume of the body is calculated.
Solution of integrals
Leibniz and Newton laid the foundations for differential and integral calculus. In the following decades, there were many great discoveries related to the calculation of integrals.
Since the integrand can take different kinds, naturally, this led to the division of integrals into their 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 the integrals in an analytical form, that is, using any known method. Of course, it's great to get an analytical solution, 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 a modern person.
Integral Solving Calculator
Now the most interesting. Some 15 years ago, a schoolboy could not even imagine that such integral calculators would be at hand, such as, for example, ours. It certainly makes the learning process easier. You can check your solutions, find mistakes and better learn the educational course.
And here we repeat once again, the calculator for solving integrals is only your trouble-free assistant, which you can turn to at any time. But not changing your head. Try to solve problems on your own, this is the only way to develop thinking, and the computer will help.
Finding the indefinite integral is a very common problem in higher mathematics and other technical branches of science. Even the solution of the simplest physical problems is often not complete without the calculation of several simple integrals. Therefore, from school age, we are taught techniques and methods for solving integrals, numerous tables with integrals of the simplest functions are given. However, over time, all this is safely forgotten, either we do not have enough time for calculations or we need to find a solution to the indefinite integral from very complex function. To solve these problems, our service will be indispensable for you, which allows you to accurately find the indefinite integral online.
Solve the indefinite integral
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