Integrate the given expression. ſ(2x + 4)2 dx 4x3 + 16x2 + 4x + c 8x+ 16 + C x3 +8x2 + 16x+C x3 + + 4x + C
13. S(3 – 2x – 4x²)(1+4x) dx 14. S Inx) dx =
Evaluate the integral. 4) S -2x cos 7x dx Integrate the function. dx (x2+36) 3/2 5) S; 5) Express the integrand as a sum of partial fractions and evaluate the integral. 7x - 10 6) S -dx x² . 44 - 12 6)
(a) i) For ∫(4x−4)(2x^2-4x+2)^4 dx (upper boundry =1, lower =0) Make the substitution u=2x^2−4x+2, and write the integrand as a function of u, ∫(4x−4)(2x^2−4x+2)^4 dx =∫ and hence solve the integral as a function of u, and then find the exact value of the definite integral. ii) Make the substitution u=e^(3x)/6, and write the integrand as a function of u. ∫ e^(3x)dx/36+e^(6x)=∫ Hence solve the integral as a function of u, including a constant of integration c, and then write...
integrate. state du and u a) tan(4x sec (4x)dr dx r +1 b) dx x +1 c) csc (3xax a) tan(4x sec (4x)dr dx r +1 b) dx x +1 c) csc (3xax
Q5). Integrate using Partial Fractions (show all working) 4x-8 dx x-2
1. Integrate. (a) Vr+3ds (b) x sin (x) cos (2x)dx
QUESTION 12 Integrate the function. а dx 2x +1 s T T T
8. Using Chain Power Rule a) ∫ (3X^2 + 4)^5(6X) dx b) ∫](2X+3)^1/2] 2dx c) ∫X^3](5X^4+11)^9 dx d ∫(5X^2(X^3-4)^1/2 dx e) ∫(2X^2-4X)^2(X-1) dx f) ∫(X^2-1)/(X^3-3X)^3 dx g) ∫(X^3+9)^3(3X^2) dx h) ∫[X^2-4X]/[X^3-6X^2+2]^1/2 dx
(1 point) Evaluate the indefinite integral. €2x sin(4x) dx = +C.