(a) \int_{0}^{1} (3x^3-5) cosx dx (b) \int_{0}^{e-1} ln(x+1) dx Evaluate the indefinite integral. Integral of (cos x)/(sin^2 x) dx. Evaluate the indefinite integral. (Use C for the constant of integration.) Integral of (sin 2x)/(1 + cos...
Evaluate the indefinite integral: (x^2 + x + 1) / ( x^3 + 2x^2 - x - 2) dx Evaluate the indefinite integral \int_0^4 (2e^x+3 \sin x) dx Evaluate the indefinite integral. \int \frac{cosx}{sin^2x} dx Evaluate the indefinite integral. \int xe^{3x} dx ...
Evaluate the integrals. A) Integral of (dx)/(2*sqrt(x) + 2x). B) Integral of tan(x) ln(cos(x)) dx. What is the antiderivative of the integral of x^(-1/2) sin 4x^(1/2) dx? Evaluate the integral: integral sec^2 x/tan^2 x + 2 tan x + 2 dx ...
We can remember the formulas of derivatives of some important functions. Here are the corresponding integrals of these functions that are remembered as standard formulas of integrals.∫ xn dx=xn+1 /n+1+C, where n ≠ -1 ∫ dx =x+C ∫ cosxdx = sinx+C ∫ sinx dx = -cosx+C ∫ sec...
The substitution of some variable in the place of trigonometric ratios is known as the trigonometric substitution. We will use the trigonometric integral to evaluate the integral of the given function. Answer and Explanation:1 Given: I=∫cot(x)dxI=∫cos(x)sin(x)dx ...
【题目】Use integration by parts to find the integral of:[Hint: In (7) write nz as 1nz and in (9) write arctanz as 1arctan .(1)x2(2) xsinx(3) x^2lnx(4)z sin3(5) xcos2x(6) xsec^2x(7)n(8) (lnx)^2(9)arctan ...
Evaluate the integral3 sin(r)sin(2r)sin(3x)dr Note: Use an upper-case "C" for the constant of integration. 相关知识点: 试题来源: 解析 ∫-3sin(x)sin(2x)sin(3x)dx =-3∫sinx⋅2sinxcosx(sinx-4sin^3x)dx =-6sin^2x(3sinx-4sin^3x)cosxdx Let, sinx= cosxdx-d2. =-6∫z^2...
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 (...
TheUniversityofSydneyMath1003IntegralCalculusandModellingSemester2ExercisesforWeek52012AssumedKnowledgeSketchingcurvesofsimplefunctions.Integralsofsimplefunctionssuchasxn(including1/x),sinx,cosx,ex.Objectives(4a)Tounderstandandbeabletouseintegrationbypartstoevaluatedefiniteintegrals.(4b)Tounderstandthatanindefinite...
2+CB34. cosxexp(sinx)dxAns:exp(sinx)+CB35. (3x+2)10dxAns:133(3x+2)11+CB36. x3(x2+1)ndxAns:(x2+1)n+22(n+2)−(x2+1)n+12(n+1)+CB37. x(x+1)95dxAns:197(x+1)97−196(x+1)96+CB38. x√2x+3dxAns:110(2x+3)5/2−12(2x+3)3/2+CB−2Productsofsinesand...