How Can U-Substitution Simplify Trigonometric Integrals?

[jtt]

Homework Statement

use substitution to evaluate the integral

Homework Equations

1)∫ tan(4x+2)dx
2)∫3(sin x)^-2 dx

The Attempt at a Solution

1) u= 4x+2 du= 4
(1/4)∫4 tan(4x+2) dx
∫(1/4)tan(4x+2)(4dx)
∫ (1/4) tanu du
(1/4)ln ltan(u)l +c

2) u=sinx du= cosx or u=x du = 1 ?

 

[haackeDc]

Homework Statement

use substitution to evaluate the integral

Homework Equations

1)∫ tan(4x+2)dx
2)∫3(sin x)^-2 dx

The Attempt at a Solution

1) u= 4x+2 du= 4
(1/4)∫4 tan(4x+2) dx
∫(1/4)tan(4x+2)(4dx)
∫ (1/4) tanu du
(1/4)ln ltan(u)l +c

2) u=sinx du= cosx or u=x du = 1 ?

Homework Statement

Homework Equations

The Attempt at a Solution

For your first integral, you evaluated ∫tan(u)du incorrectly.
∫tan(u) du = ∫sin(u)/cos(u) du
= -∫-sin(u)/cos(u) du
So now solve for this integral, given that ∫f'(x)/f(x) dx = ln(|f(x)|) + c

For your second, I'm not sure why you would use 'u' substitution,
because 1/sin^2(x) = csc^2(x), which has the integral of -cot(x) + c.

I'll leave that to you to find a way with u-substitution.