How do you find $\int 1 - {tan x}^{2} d x$ $int 1-tanx^2dx$ ?

Question

How do you find $\int 1 - {tan x}^{2} d x$ $int 1-tanx^2dx$ ?

1 Answer

Related questions

How do I evaluate the indefinite integral $\int {sin}^{3} (x) \cdot {cos}^{2} (x) d x$ $intsin^3(x)*cos^2(x)dx$ ?
How do I evaluate the indefinite integral $\int {sin}^{6} (x) \cdot {cos}^{3} (x) d x$ $intsin^6(x)*cos^3(x)dx$ ?
How do I evaluate the indefinite integral $\int {cos}^{5} (x) d x$ $intcos^5(x)dx$ ?
How do I evaluate the indefinite integral $\int {sin}^{2} (2 t) d t$ $intsin^2(2t)dt$ ?
How do I evaluate the indefinite integral $\int {(1 + cos (x))}^{2} d x$ $int(1+cos(x))^2dx$ ?
How do I evaluate the indefinite integral $\int {sec}^{2} (x) \cdot tan (x) d x$ $intsec^2(x)*tan(x)dx$ ?
How do I evaluate the indefinite integral $\int {cot}^{5} (x) \cdot {sin}^{4} (x) d x$ $intcot^5(x)*sin^4(x)dx$ ?
How do I evaluate the indefinite integral $\int {tan}^{2} (x) d x$ $inttan^2(x)dx$ ?
How do I evaluate the indefinite integral $\int {({tan}^{2} (x) + {tan}^{4} (x))}^{2} d x$ $int(tan^2(x)+tan^4(x))^2dx$ ?
How do I evaluate the indefinite integral $\int x \cdot sin (x) \cdot tan (x) d x$ $intx*sin(x)*tan(x)dx$ ?

Impact of this question

1778 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-12-03T01:18:31

$\int (1 - {tan}^{2} x) d x = 2 x - tan x + C$ $int(1-tan^2x)dx = 2x- tan x +C$

Explanation:

We can start of by doing the following

$\int 1 - {tan}^{2} x d x = \int 1 d x - \int {tan}^{2} x d x$ $int 1-tan^2x dx = int 1 dx - int tan^2x dx$

Then integrate the first integral

$= x - \int ({sec}^{2} x - 1) d x$ $= x- int(sec^2x -1)dx$

Rewrite using trigonometric identity

${tan}^{2} x = {sec}^{2} x - 1$ $color(red)(tan^2 x = sec^2x - 1)$

$= x - [\int ({sec}^{2} x) d x - \int 1 d x]$ $= x- [int(sec^2x) dx -int1dx]$
$\int ({sec}^{2} x d x = tan x + C)$ $color(red)(int (sec^2x dx= tan x + C)$

$= x - [tan x - x] + C$ $= x- [ tan x -x] +C$

$= 2 x - tan x + C$ $= 2x- tan x +C$

Science

Math

Humanities

... and beyond

How do you find $\int 1 - {tan x}^{2} d x$ $int 1-tanx^2dx$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you find int 1-tanx^2dx∫1−tanx2dxint 1-tanx^2dx?

1 Answer

Explanation:

Related questions

Impact of this question

How do you find $\int 1 - {tan x}^{2} d x$ $int 1-tanx^2dx$ ?