(1)xe^x-e^x+c(2)-xcosx+sinx+c(3)1/3x^3lnx-1/9x^3-c(4)-1/3πccos3x+1/9sin3x-c(5)1/2xsin2x⋅|1/4cos2x|c(6)xtanx+ln(cosx)+c(7)xlnx-x+c(8)x(lnx)^2-2xlnx+2x+c(9)αarctana1/2ln(a^2)1e 结果一 题目 Use integration by parts
The process of finding the integral of the composition of two or more functions by taking them function one and function two is known as the integration by parts. The following formula is known as the integration by parts formula ∫f(x)g(x)dx=f(x)∫g(x)dx−∫(f′(x)∫g(x)dx)...
Use the integration by parts process to find the antiderivative of: f(x) = e^{2x}\sin x. Use Integration to prove the following equataion is true Intergral of dx/(e^{(2x)}-4e^x)+4 = (x/4) + (\ln(e^{(2x)}-2)...
Given F(x) = \int_1^x \frac{1}{t^2} \; dt, (a) integrate to find F as a function of x, and (b) demonstrate the Second Fundamental Theorem of Calculus by differentiating the result in part (a). Given F(x) = \int_0^x (t + 2) \; dt, ...
For the following integral determine u and v' according to the method of integration by parts: \int (\cos(3x))^{2}dx Find the reduction formula for the integral: \int cos^n(4 x) dx. Derive the integration reduction formula for integral (tanx)^ndx. Integrate by parts....
Derive the integration reduction formula for integral (tanx)^ndx. Use basic integration formulas to find the integral of cos 2x dx. Find a reduction formula for \int (1 - x^{2})^{n/2} dx using integration by parts, and th...
\int x \tan^{-1} x^2\ dx. (a) Prove the reduction formula: The integral of cos^n x dx = 1/n cos^(n-1) x sin x + (n-1)/n integral of cos^(n-2) x dx (b) Use part (a) to evaluate the integral of cos^2 x dx; integral of cos^4 ...