What's the integral of $\int {(csc x)}^{2} d x$ $int (cscx)^2 dx$ ?

Question

What's the integral of $\int {(csc x)}^{2} d x$ $int (cscx)^2 dx$ ?

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

12511 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-11-02T17:04:49

$\int {(csc x)}^{2} d x = - cot x + C$ $int (cscx)^2 dx = -cotx+C$

Explanation:

The derivative of $cot x$ $cotx$ is ${csc}^{2} x$ $csc^2x$ ,

so the integral of ${csc}^{2} x$ $csc^2x$ is $cot x + C$ $cotx + C$

If you really want the integral of the integral, then use:

$\int [\int {(csc x)}^{2} d x] d x = \int [- cot x + C] d x$ $int[int (cscx)^2 dx] dx = int [-cotx+C] dx$ where $C$ $C$ is an arbitrary constant

$= \int (- \frac{cos x}{sin x} + C) d x$ $= int (-cosx/sinx + C) dx$ where $C$ $C$ is an arbitrary constant

$= - ln | sin x | + C x + D$ $= -lnabssinx + Cx +D$ where $C, D$ $C,D$ are arbitrary constants

$= ln | csc x | + C x + D$ $= lnabscscx + Cx +D$ where $C, D$ $C,D$ are arbitrary constants

Science

Math

Humanities

... and beyond

What's the integral of $\int {(csc x)}^{2} d x$ $int (cscx)^2 dx$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

What's the integral of int (cscx)^2 dx∫(cscx)2dxint (cscx)^2 dx?

1 Answer

Explanation:

Related questions

Impact of this question

What's the integral of $\int {(csc x)}^{2} d x$ $int (cscx)^2 dx$ ?