How do you integrate $\int \frac{{tan}^{- 1} x}{x^{2} + 1}$ $int tan^-1x/(x^2+1)$ by trigonometric substitution?

Question

How do you integrate $\int \frac{{tan}^{- 1} x}{x^{2} + 1}$ $int tan^-1x/(x^2+1)$ by trigonometric substitution?

1 Answer

Related questions

How do you find the integral $\int \frac{1}{x^{2} \cdot \sqrt{x^{2} - 9}} d x$ $int1/(x^2*sqrt(x^2-9))dx$ ?
How do you find the integral $\int \frac{x^{3}}{\sqrt{x^{2} + 9}} d x$ $intx^3/(sqrt(x^2+9))dx$ ?
How do you find the integral $\int x^{3} \cdot \sqrt{9 - x^{2}} d x$ $intx^3*sqrt(9-x^2)dx$ ?
How do you find the integral $\int \frac{x^{3}}{\sqrt{16 - x^{2}}} d x$ $intx^3/(sqrt(16-x^2))dx$ ?
How do you find the integral $\int \frac{\sqrt{x^{2} - 1}}{x} d x$ $intsqrt(x^2-1)/xdx$ ?
How do you find the integral $\int \frac{\sqrt{x^{2} - 9}}{x^{3}} d x$ $intsqrt(x^2-9)/x^3dx$ ?
How do you find the integral $\int \frac{x}{\sqrt{x^{2} + x + 1}} d x$ $intx/(sqrt(x^2+x+1))dx$ ?
How do you find the integral $\int \frac{d t}{\sqrt{t^{2} - 6 t + 13}}$ $intdt/(sqrt(t^2-6t+13))$ ?
How do you find the integral $\int x \cdot \sqrt{1 - x^{4}} d x$ $intx*sqrt(1-x^4)dx$ ?
How do you prove the integral formula $\int \frac{d x}{\sqrt{x^{2} + a^{2}}} = ln (x + \sqrt{x^{2} + a^{2}}) + C$ $intdx/(sqrt(x^2+a^2)) = ln(x+sqrt(x^2+a^2))+ C$ ?

Impact of this question

1472 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-09T13:56:04

The answer is $= \frac{{(arctan x)}^{2}}{2} + C$ $=(arctanx)^2/2+C$

Explanation:

Apply the substitution

$u = arctan x$ $u=arctanx$ , $\Rightarrow$ $=>$ , $d u = \frac{d x}{1 + x^{2}}$ $du=(dx)/(1+x^2)$

Therefore,

$\int \frac{arctan x d x}{1 + x^{2}} = \int \frac{u \cdot (1 + x^{2}) d u}{1 + x^{2}} = \int u d u$ $int(arctanxdx)/(1+x^2)=int(u*(1+x^2)du)/(1+x^2)=intudu$

$= \frac{u^{2}}{2}$ $=u^2/2$

$= \frac{{(arctan x)}^{2}}{2} + C$ $=(arctanx)^2/2+C$

Science

Math

Humanities

... and beyond

How do you integrate $\int \frac{{tan}^{- 1} x}{x^{2} + 1}$ $int tan^-1x/(x^2+1)$ by trigonometric substitution?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you integrate ∫tan−1xx2+1int tan^-1x/(x^2+1) by trigonometric substitution?

1 Answer

Explanation:

Related questions

Impact of this question

How do you integrate $\int \frac{{tan}^{- 1} x}{x^{2} + 1}$ $int tan^-1x/(x^2+1)$ by trigonometric substitution?