Since f(x)=\int xe^{-x^{2}}\d x, let u=-x^2, \d u=-2x\d x or \dfrac {-\d u}{2}=x\d x. Thus, f(x)=\int e^{u}\left(-\dfrac {\d u}{2}\right)=-\dfrac {1}{2}e^{u}+C=-\dfrac {1}{2}e^{-x^{2}}+C and f(0)=1 ⇒ - 12(e^0)+C=...
{eq}\int xe^{x^2} dx {/eq}Antiderivative of a Function:The antiderivative of {eq}\displaystyle f(x) {/eq} is {eq}F(x) = \int f(x) \ dx {/eq}. To compute the indefinite integral, we'll take the help of substitution. Integration by substitution is a process of ...
Question: Find the antiderivative of {eq}\int_{1}^{3}x^2dx {/eq} Integration: Consider a function {eq}\displaystyle f(x) {/eq} with upper limit {eq}\displaystyle b {/eq} and lower limit {eq}\displaystyle a {/eq} Then integral is written as {eq}\displaystyle \int _a^b f(x)...
The antiderivative of {eq}H(x) {/eq} is {eq}h(x) {/eq} whose derivative is equal to the original function. Mathematically: {eq}\int H(x) dx=h(x)+C {/eq}Answer and Explanation: We have to find the antiderivative of {eq}\displaystyle{ \rm F(x)=x(4-x)^2. } {/eq} Th...
Find an antiderivative F(x) of f(x) = 11x - \sqrt x. Find the antiderivative for f(x) = \frac{2x^2 + x + 9}{(x - 1)(x^2 + 3)} Find the antiderivative f(x) = 2 x^{-4} for x > 0 Find an antiderivative F(x) with F'(x) = f(x) and F(0) = 0...
f(x)=11+x2 Question:Find the antiderivative of the following function. f(x)=11+x2Answer and Explanation:The antiderivative of the function f(x) is another function F(x) such that, F′(x)=f(x). The existence of the antiderivative is guaranteed if the function f(x) is...
Answer to: Find the Antiderivative of: \int \frac{1}{10 + x^{2} + 2x} By signing up, you'll get thousands of step-by-step solutions to your...
1) Evaluate Integral (sec x tan x + e^{-x} ) dx 2) Find the area of the region bounded by the curves y = x^2 and y = x^3 - 2x. 1) Find the area of the region bounded by the given curves. ...
∫secx(secx+tanx)dx=+C Anti-derivative of Trigonometric Functions: The mathematical formulas of the anti-derivative (with respect to the variable t) for the integrands that contain secant and tangent trigonometric functions are: ∫sec2t dt=tant+C∫secttan...
Answer to: Find the antiderivative. \int \dfrac{x-3}{x^2-6x+5}dx By signing up, you'll get thousands of step-by-step solutions to your homework...