I=∫sec2x(secx+tanx)9/2dx, we will use the substitution t=secx+tanx. Step 1: Substitute t=secx+tanx From the identity sec2x=1+tan2x and the derivative of t: dtdx=secxtanx+sec2x=sec2x+secxtanx. Thus, we can express dx in terms of dt: dx=dtsec2x+secxtanx. Step 2: Rewrite se...
Evaluate the integral. \int \tan x \sec^2x dxSolve the integral. integral sec^2 x tan x dxFind the integral of (sec^2 x)/(sqrt(tan x)) dx.Evaluate the following integral. Integral tan^3 x sec^2 x dxFind the antiderivative of the following function. f(x) =...
Answer to: Evaluate the integral: integral sec(x) squareroot sec(x) + tan(x) dx By signing up, you'll get thousands of step-by-step solutions to...
Evaluate the integral: integral of 2x^(-1) ln(x^(3/2)) dx. Evaluate the integral. Integral from sqrt(2)/4 to 1/2 of dx/(x^5 sqrt(16x^2 - 1)). Evaluate the integral: integral of 1/x cos(ln x) dx. Evaluate the integral x2sqrt(2+x) Evaluate the integral. I=\int...
常用积分表（Common integral table）Common integral formula (a) containing the integral (axb+0a =) Formula 1.dxaxb+ = 1lnaxbCa++ 2. = (axbx) + 11 (formula)(1)AxbCa + + + Mu + (U = 1.)3.dxxaxb+ = formula 21 (LN) axbbaxbCa+.++ The 4.2dxxaxb+ formula (2) = 22311 (...
88.cscdxx∫=lntan2xc + =lncsccotxxc. + 89.2secdxx∫=tanxc + 90.2cscdxx∫=cotxc. + 91.sectandxxx∫=secxc + 92.csccotdxxx∫=cscxc. + 93.2sindxx∫=1sin224xxc. + 94.2cosdxx∫=1sin224xxc + + 95.sindnxx∫=1211sincossindnnnxxxnn... ...
Question: Evaluate: ∫0ln(10)∫ex10(1ln(y))dydx Double Integrals: Recall that there is always another way to set up a double integral. So when we have one like the above, that would usually result in us looking at a table of integrals, we can always try flipping the order, as ...
Evaluate the integral: ∫02ln(1+t)dt Integration by Parts for Definite Integrals: The integration by parts formula for definite integrals is: ∫x=abudv=(uv|x=ab−∫x=abvdu. This formula can be proved by using the fundamental theorem of calculus along with the product rule for deriva...
We apply the following rules of integration: ∫exdx=ex∫cos(x)dx=sin(x) Answer and Explanation:1 We have to evaluate the definite integral. ∫023ex+2cos(x)dx {eq}\begin{align} \int_{0}^{2}3e^{x} +... Learn more about this topic: ...
Evaluate the integral.xsecxtanxdx Given the equation y ln (x^2 + y^3 + 4) = 9, evaluate dy / dx. Evaluate: cosec^{-1} (-2) Find F(x) = \int_2^x (t^3 + 2t - 2) \; dt and evaluate it at x = 2, x = 5, and x = 8. ...