Question

Tan(2-3x)dx in tegration ​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Correct Question

Integrate ∫tan(2-3x)dx​

Answer

Therefore, integration of ∫tan(2-3x)dx​ is $\frac{-sec^{2}(2-3x) }{3} + C$, where C is an arbitrary constant.

Given

∫tan(2-3x)dx​

To Find

Integrand of ∫tan(2-3x)dx​

Solution

I = ∫tan(2-3x)dx​                                               [1]

Let z = 2 - 3x                                                  [2]

Differentiating with respect to x we get,

dz/dx = -3

or, -3dx = dz

or, dx= -dz/3                                                     [3]

From equation [1], [2], and [3] we get,

I = ∫-(tanz/3)dz

We know that ∫cvdv = c∫vdv, where c is a constant and v is the variable.

Therefore,

I = -1/3∫tanz dz

We know that ∫tanv dv = sec²v + C

Therefore,

$I = \frac{-sec^{2}(z) }{3} + C$, where C is an arbitrary constant.

Now putting the value of z we get

$I = \frac{-sec^{2}(2-3x) }{3} + C$

Therefore, integration of ∫tan(2-3x)dx​ is $\frac{-sec^{2}(2-3x) }{3} + C$, where C is an arbitrary constant.

#SPJ2