Integrate the functions in Exercises: e^ ^ -1 x 1+x^2 - Vidyadip

Question

Integrate the functions in Exercises:
$\frac{\text{e}^{\tan^{-1}\text {x}}}{1+\text{x}^2}$

✓

Answer

$\text{Let I}=\int\frac{\text{e}^{\tan^{-1}\text{x}}}{1+\text{x}^2}\text{ dx} \ \ \ \ \ \ \ ...\text{(i)} $
$\text{Putting }\tan^{-1}\text{x}=\text{t}\ \ \ \Rightarrow \ \ \ \frac{1}{1+\text{x}^2}=\frac{\text{dt}}{\text{dx}}\ \ \ \ \Rightarrow \ \ \ \ \frac{\text{dx}}{1+\text{x}^2}=\text{ dt} $
$\therefore \ \ \ \ $From eq. (i), $\text{I}=\int\text{e}^{\text{t}}\text{ dt}=\text{e}^{\text{t}}+\text{c}=\text{e}^{{\tan}^{-1}\text{x}}+\text{c}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "1 Marks Question" from INTEGRALS→INTEGRALS — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Write the value of sin $\Bigg[\frac{\pi}{3}-\sin^{-1}\Big(-\frac{1}{2}\Big)\Bigg]$

Integrate the function $\frac{\sin x}{\sin (x-a)}$

Evaluate $\int_0^1 \frac{\left(x^2-x\right)}{\sqrt{x}} d x$.

For what value of x, is the matrix A =$\begin{bmatrix} 0 & 1 & -2 \\ -1 & 0 & 3 \\ \text{x} & -3 & 0 \end{bmatrix}$ a skew-symmetric matrix?

Write the matrix form $\left[\begin{array}{lll}5 & 3 & 1 \\ 2 & 1 & 3 \\ 1 & 2 & 4\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}16 \\ 19 \\ 25\end{array}\right]$ is system of equations.

If X and Y are 2 × 2 matrices, then solve the following matrix equations for X and Y.
$2\text{X}+3\text{Y}=\begin{bmatrix}2&3\\4&0\end{bmatrix},\ 3\text{X}+2\text{Y}\begin{bmatrix}-2&2\\1&-5\end{bmatrix}$

The Integrating Factor of the differential equation $\left(1-y^{2}\right) \frac{d x}{d y}+y x=a y~(-1<y<1)$ is

Integrate the functions in Exercises:
$\frac{\sin^{-1}\text{x}}{\sqrt{1-\text{x}^2}}$

Integrate the functions in Exercises:
$\frac{\cos\sqrt{\text{x}}}{\sqrt{\text{x}}}$

Let the vectors $\vec a\;$ and $\vec b$ be such that $\left| {\vec a} \right| = 3\;$ and $\;\left| b \right| = \frac{{\sqrt 2 }}{3},\;$ then $\;\vec a \times \vec b$ is a unit vector if the angle between $\vec a\;$ and $\vec b\;$ is