when integrating 1/16(sint^2)/(cost) how do you simplify/solve this equation? Please show steps and assumption

Answer 1

I assume you mean integrate (1/16)(sin²t)/(cost).

First rearrange the expression to make it easier to integrate.

(1/16)(sin²t)/(cost) = (1/16)(1 - cos²t)/cost
= (1/16)(sect - cost)

Now we can integrate.

∫(1/16)(sin²t)/(cost) = (1/16)∫(sect - cost)dt
= (1/16){ln|sect + tant| - sint} + C

Answer 2

Integral ( (1/16) [sin^2(t) / cos(t)] dt)

First, convert sin^2(t) into 1 - cos^2(t). Also, pull the constant (1/16) out of the integral.

(1/16) Integral ( [1 - cos^2(t)] / cos(t) dt)

Now, split into two fractions.

(1/16) Integral ( [1/cos(t) - cos^2(t)/cos(t)] dt )

Simplify each term.

(1/16) Integral ( [ sec(t) - cos(t) ] dt)

Integrate each term. Note that the integral of secant is worthy to memorize; the answer is ln|sec(t) + tan(t)|

(1/16) [ ln|sec(t) + tan(t)| - sin(t) ] + C

(1/16) ln|sec(t) + tan(t)| - (1/16) sin(t) + C

Answer 3

3 – (x+5) = 3x + 6 a million) Distribute the damaging --- 3 - x -5 = 3x + 6 2) Simplify --- -x - 2 = 3x + 6 3) upload x from both aspect --- -x (+x) - 2 = 3x (+x) + 6 ---> -2 = 2x + 6 4) Subtract 6 from both aspect -2 (-6) = 2x + 6 (-6) ---> -8 = 2x 5) Divide through 2 -8 (/2) = 2x (/2) x = -4