Determine the following integrals using substitution method:

(a)4x³(4x⁴+ 10)dx

(b)(6x - 5)^-7dx

2. Determine the following integrals using Integration by Parts:

(a)10x(x- 5)⁴dx

(b)xe^4Xdx

3. Assume an asset's price movement as follows:

A_t= 100 + 2Z_t

whereZt=X1+X2+... +Xtis the simple random walk with each Xibeing either+1or -1with equal probability such as fair coin flips. Calculate the mean, variance and standard deviation of this asset whent= 3.