Find the indefinite integral. {eq}\displaystyle \int \frac{t}{t^4 + 1}dt {/eq} Integrals: We have an indefinite integral that has an integrand that has a linear and a polynomial of degree four as the integrand. To evaluate the antiderivative we just need to apply the substitution ...
Find the indefinite integral, and check your answer by differentiation. {eq}\int {\left( {6x - 1} \right){{\left( {x + 2} \right)}^2} \ dx} {/eq} Integration Properties: Not-defined integrals have the following properties: 1) {eq}\displaystyle \int (f(...
definite (indefinite) integral 定(不定)积分. 属类:英汉句库-- A definite integral is anindefiniteintegral evaluated over an interval. The result is not affected by the choice for the value of C. 定积分是区间上的不定积分值。结果不受C值选择的影响。
integral indefinite... noun Words related to indefinite integral nounthe set of functions F(x) + C, where C is any real number, such that F(x) is the integral of f(x) Related Words integral Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex In...
Integration is the reverse process of differentiation so we can also call it as antiderivative. There is one more name for it, that is Primitive. If f & g are functions of x such that g'(x) = f(x) then the function g is called a Primitive Or Antiderivative Or Integral of f(x) ...
Find the indefinite integral. {eq}\int \frac{1}{5x^7} {/eq} dxIntegrals:We have an integral whose integrand has a polynomial of the degree seven as the denominator. We will apply the standard property and the standard integral formula to solve the integral. We will put a constant of ...
The only assumption on k is that it satisfies a linear differential equation with polynomial coefficients. The approximate value of the integral is given in terms of Chebyshev coefficients of functions that form a solution of a certain system of differential equations. As an illustration, we ...
Find the indefinite integral. {eq}\int x^3 e^{5x^2} \, \mathrm{d}x {/eq} Integrals: We have an integrand which is a product of a polynomial function and an exponential function. We will apply the substitution first and then apply the integration by parts. Then we apply the const...
Why is it called indefinite integral? The indefinite integral of the function is the set of all antiderivatives of a function. It is customary to include the constant C to indicate that there are an infinite number of antiderivatives.
Find the indefinite integral: ∫(x3+4x2−5x)dxIntegrating Polynomials:To integrate any polynomial P(x), we need the following two rules. 1) The linearity rule for integrals: ∫[af(x)+bg(x)]dx=a∫f(x)dx+b∫g(x)dx.2) The power rule for integrals: if n≠−1, then ...