please solve this one
calculus 2
please solve this one calculus 2 QUESTION 4 Evaluate the integral by using a substitution prior...
Apply integration by parts twice to evaluate the integral. ſ in?(x15) dx correct value of ſin?(x+5) Choose the dx below. O A. x In? (x45) - 30x In (x15) + 15x + C O B. xIn? (x15) - 30x In (x15) + 450x+C O c. xIn(x15) + 450x In (x15) - 30x+C OD. xIn? (x+5) - 450x In (x15) + 450x + c
Evaluate the following integral. This involves substitution and integration of ln. \int 3 2 (x ^4 + 1 )/(x ^5 + 5x )dx
help please Evaluate the definite integral using the Fundamental Theorem of Calculus. (1+ (1 + 14х5) dx Use The Fundamental Theorem of Calculus and the antiderivative found in Step 2 to evaluate the definite integral. fo* (2 + 14x5) dx = = (x+3x0916 (1+](O* )-( O*+O) “) 10 3
3. State whether the given integrals should be solved using Integration by Parts or u-Substitution. but do NOT solve them. /2"(34) de (b) / (+ 3)e+ dr (c) (a) / 1+ ** (42") der (2+1)* (x + 1)(x + 2) dr (e) 4. Evaluate each integral using t-Substitution da (b) / (+" - 13% (26) ds
(a) Use Trigonometric Substitution to evaluate the integral 22 9 dr. T (b) Use the method of Integration by Parts to rewrite the following integral. (You do not need to fully evaluate the integral.) | «* sin(x2) dr. (c) Find the form of the partial fraction decomposition of 2.r2 - 3.c + 77 (x - 1)(x² +2) (You do not need to solve for the coefficients.)
solve 1 and 2. Evaluate the integral. 3T/4 1) rt/4 D) o B)-16 C) Find the derivative of the integral using the Second Fundamental Theorem of Calculus 2) y- cos nt dt D) cos (3)-1 C) sin (3) B) cos (x3) A) 6x5 cos (x3) Evaluate the integral. 3T/4 1) rt/4 D) o B)-16 C) Find the derivative of the integral using the Second Fundamental Theorem of Calculus 2) y- cos nt dt D) cos (3)-1 C) sin (3) B)...
2. (20 points) Evaluate the following integral using Integration by Parts or Trigonometric Substitution dr Show all your work: i.e. If you use Integration by Parts, clearly define u,du, v, dv or if you use Trig Sub clearly define what substitution you use for r as well as dr and other corresponding parts of your substitution
solve using the fundamental law of calculus if applicable Evaluate the definite integral La 2e (Inx) dx x
Question 4 a) Differentiate with respect to x, i. y = sin 2x ii. y = x In(5x + 2) b) Show that if y = cotx, dy dx -cosec? x c) Show that if y = tan x, then dy dx 1 1+xal Question 5 Use calculus to find any turning points of the function A(t) = te-020 and determine their nature (maximum, minimum or inflexion) using any method. Question 6 a) Find tan” x dx b) Use integration...
Can you solve the question with using Calculus of residues. Method is described in the Complex Analysis book of Serge Lang. Please do not solve with partial integral. Thanks. ral Evaluate the following definite real integ IC dx e"- e ral Evaluate the following definite real integ IC dx e"- e