-2 7 dx (d) 2 + cos (x)

Use De Moivre's Theorem to find the fourth root of Z = 8i(3 + v2).

e)f [cot2x√sin2x + cos2x]dx

a) Rewrite A = √=x² + 4x + 21 in the form A V 6² - (x − a)². b) Use a trigonometric substitution to evaluate the indefinite integral. S/ dx You must show all steps.

integrate

> [1] [(4x³ + x)v4x² + 1dx > [2] S(2x7/2 – Vx)* dx > [3] S V1+ 2sin3xcos3xdx > [4] [(x + 2)Vx + 3dx > [5] S sin³xdx Hint: Kindly use trigonometric identities to convert the expression in the form Asinx+Bsin3x

Q2) Verify v(x.y)-3x²y-y+5x is harmonic in the entire complex plane then find the conjucte harmonic function of v.

Use complex analysis methods to find cos 2x 5 + 4 cos x I: 2π dx.

Let z=x+ iy with x and y are real. What is the imaginary part of sin (x + iy)

find the arbitrary constants