Evaluate the integral. I=\int x^2 \sqrt{2-x} dx Evaluate the following integral. Integral of e^(x + y^2 - z) dx dy dz over x from ln(4y) to ln(5y), y from 1 to sqrt(z), z from 1 to ln(16). Evaluate the integral. tan3xsecxdx ...
To solve this problem, we'll use integration by substitution, which is also called u-substitution and we'll also use the trigonometric identity sec2x−1=tan2xAnswer and Explanation: ∫tan3(x)sec2(x)dx =∫tan2xtanxsec2x dx Now we know......
∫f(g(x))g′(x)dx=∫f(u)duwhenu=g(x) Also, we will be using the derivative of the tangent trig function. d(tanx)dx=sec2x Answer and Explanation:1 ∫tan(3x)sec2(3x)etan2(3x)dx. First we will perform ausubstitution. ...
Evaluate the integral. integral 20 / (2 x + 9)^3 dx Evaluate the integral: integral 9/sqrt(9x^2 + 6x - 8) dx Evaluate the integral. Integral of 5sec^3(x) tan(x) dx. Evaluate the integral: integral of 1/(x^2) sqrt(2 - 3/x) dx from 2 to 3. ...
(∫ (sec)(x)+(tan)(x)dx) 相关知识点: 试题来源: 解析 Split the single integral into multipleintegrals. (∫ (sec)(x)dx+∫ (tan)(x)dx) The integral of ( (sec)(x)) with respect to ( x) is ( (ln)(|(sec)(x)+(tan)(x)|)). ( (ln)(|(sec)(x)+(tan)(x)|)+C+∫...
3.Apply the integral: Since the derivative of sec(x) is sec(x) * tan(x), we can conclude that: where C is the constant of integration. 4.Final result: Thus, the final result of the integral is: 1cos(x) Integral Calculatorcomputes an indefinite integral (anti-derivative) of a functi...
Integral of sec(x)^2 by x: tan(x)+C To compute the integral of sec(x)^2 with respect to x, follow these steps: 1.Identify the integral: We want to compute the integral ∫ sec(x)^2 dx. 2.Recall the antiderivative: The antiderivative of sec(x)^2 is a well-known result. It ...
∫ tan^3x/cos^4xdx =∫ tan^3x*sec^4xdx =∫ tan^3x*(tan^2x+1)*sec^2xdx 令u=tanx du=sec^2xdx =∫u^3(u^2+1)du =∫(u^5+u^3)du =1/6u^6+1/4u^4+C =1/6 tan^6x+1/4tan^4x+C
∫ sec x (tan x) dx = sec x + C ∫ csc x ( cot x) dx = – csc x + C ∫ (1/x) dx = ln |x| + C ∫ exdx = ex+ C ∫ axdx = (ax/ln a) + C ; a>0, a≠1 These integral formulas are equally important asdifferentiation formulas. Some other important integration for...
CLR + – × ÷ ^ √ f(x) π ( ) √ 3√ 4√ n√ You can also input:• sqrt(…)• root(n, …) ln log10 logn exp ex abs |x| sin cos tan csc sec cot arcsin sin-1 arccos cos-1 arctan tan-1 arccsc csc-1 arcsec sec-1 arccot cot-1 sinh cosh tanh csch sech co...