Please help me with these few equations its not much Identify u. du. and the for

Question

Please help me with these few equations its not much

Identify u. du. and the formula from a table of integrals that would be used so compete the integration. Do not integrate. What are the values of u and du? Give the proper trigonometric substitution and find the transformed integral, but do not integrate. The proper substitution is x = . (Type an expression using 0 as the variable.) Integrate the function by using a table of integrals. What is the number corresponding to the appropriate formula from the table of integrals? Integrate the function by using a table of integrals. What is the number corresponding to the appropriate formula from the table of integrals? Evaluate . Use a table of integrals to find the indefinite integral. Use C as the binary constant.)

Explanation / Answer

1)u= x^2 du=2xdx

2)I= dx/ (x^2 * sqrt(x^2+4))

put x=2tant hence dx=2sec^2t dt

I= 2sec^2tdt/(4tan^2t sqrt(4+4tan^2t)) = (4cost/ sin^2t) dt

3) Put 4+x= u du=dx and x=u-4

I= 5x sqrt(4+x)dx = 5(u-4) sqrt(u)du

on proceeding further

Int(5x sqrt(4+x)) = 2/3 (x+4)^(3/2) (3x-8) + constant

put the limits and I= 3712/3

4)Int( 4x e^(3x)dx)

use integration by parts

Int(u.dv) = u.v - Int(v.du)

put u=x and dv=4.e^(3x)

I= 4/9 * e^(3x)*(3x-1) + constant

5)Int( 1/ (x* sqrt(16x^2 + 9))) = 1/3 (log(x)-log(3+sqrt(9+16 x^2)))

6)I = dx/ [x^2(x^2-100)]

put x^2 - 100 = u^2

xdx=udu

on simplifying the expression

I= du/(u^2+100)^(3/2)

and now put u=10 tant

and the expression turns out to be I= cost dt/100

now you can calculate easily.

7)I=1/ x sqrt(9-x^2) dx

put x=3sint

I= 3cost dt/ sint.3cost

I=dt/sint =cosect dt = log(sin(t/2))-log(cos(t/2)) + constant

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