Evaluate the integral: integral tan x (1 + sec^4 x)^{3 / 2} dx. Integrate: integral of (sec^2 x)/(3 + tan^2 x) dx. Evaluate the following integral. (a) \int sec^2x \space tanx dx (b) \int (x^3 +x)^{10}(3x^2 + 1) dx Find the antiderivative of the following fun...
∫tanxln(cosx)dx Rewrite the given integral as follows, {eq}... Learn more about this topic: U-Substitution for Integration | Formula, Steps & Examples from Chapter 12/ Lesson 13 29K In this lesson, learn the technique of integration by u-substitution, its step-by-step metho...
∫ sin x dx = -cos x + C ∫ sec2x dx = tan x + C ∫ cosec2x dx = -cot x + C ∫ sec2x dx = tanx + C ∫ sec x tan x dx = sec x + C ∫ cosec x cot x dx = -cosec x + C ∫1/(√(1-x2))= sin-1x + C ∫-1/(√(1-x2))= cos-1x + C ∫1/(1+x...
(4d)Tobeabletosketchafunctionde,nedbyanintegral.(4e)Tobeabletoderiveareductionformulaforanintegral. PreparatoryQuestions 1.(i)Findtheinde,niteintegral,tanxdx. Hint:Usetanx=sinxandsubstituteu=cosx.cosx (ii)Usetwointegrationbypartto,ndtheinde,niteintegral,x2exdx. ...
Use the formula for the area of a trapezoid to evaluate ∫42(2x+3)dx∫24(2x+3)dx. Show Solution Hint Graph the function f(x)f(x) and calculate the area under the function on the interval [2,4][2,4].Area and the Definite Integral When we defined the definite integral, we lifted...
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 (...
Formula1.dxaxb+=1lnaxbCa++ 2.=(axbx)+11(formula) (1) AxbCa+++Mu + (U=1.) 3.dxxaxb+=formula 21(LN)axbbaxbCa+.++ The4.2dxxaxb+formula(2)=22311 (ln2axbbaxbbaxbCa..+.++++.)... Five (d) Formulaxxaxb+=1lnaxbCbx+ ...
Evaluate the integral of e^(x^2) dx. Evaluate the integral. \ \int 4x e^x dx Evaluate the integral. \int \frac{sin(tanx)}{cos^2x} dx Evaluate the integral of x(x + 5)^8 dx. Evaluate the integral of tan^(10)(x) sec^2(x) dx. Evaluate the integral of (x - 1/(2x))^...
Evaluate the integral \int \frac{1}{x^3 + x^2 + x + 1}\ dx Evaluate the following integral: \int (z^3-3z^2)dz. Evaluate the integral. \int \frac{dx}{x(x^2-6x-7)} Evaluate the integral. \int \frac{sec^2x}{tan^2x+9tanx+20} dx Evaluate the integral \...
(4e)Tobeabletoderiveareductionformulaforanintegral. PreparatoryQuestions 1.(i)Findtheindefiniteintegral tanxdx. Hint:Usetanx= sinx cosx andsubstituteu=cosx. (ii)Usetwointegrationbyparttofindtheindefiniteintegral x 2 e x dx. PracticeQuestions 2.Evaluatethefollowingintegralsbyusingintegrationbypart...