Evaluate e^ ^ -1x 1+x^2 dx - Vidyadip

Question

Evaluate $\int\frac{\text{e}^{\tan^{-1\text{x}}}}{1+\text{x}^2}\text{ dx}$

✓

Answer

Let $\tan^{-1}\text{x}=\text{t}$
$\frac{1}{1+\text{x}^2}\text{ dx}=\text{dt}$
Let $\text{I}=\int\frac{\text{e}^{\tan^{-1\text{x}}}}{1+\text{x}^2}\text{ dx}$
$=\int\text{e}^{\text{t}}\text{dt}$
$=\text{e}^{\text{t}}+\text{C}$
$=\text{e}^{\tan^{-1}}\text{x}+\text{C}$

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 "Solve the Following Question.(2 Marks)" from Indefinite Integrals→Indefinite Integrals — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Using the rules in logic, write the negations of the following : p ∧ (q ∨ r)

If $f: R \rightarrow R$ is given by $f(x)=x^3$, write $f^{-1}(1)$.

Integrate the following functions w. r. t. x

$\int \frac{1}{\cos x-\sin x} \cdot d x$

If the statement p, q are the statements and r, s are false statements, then determine the truth value of the statement pattern :
$(q \wedge r) \vee(\sim p \wedge s)$

The displacement ' $s$ ' of a moving particle at time ' $t$ ' is given by $s=5+20 t-2 t^2$. Find its acceleration when the velocity is zero.

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

Evaluate:
$\sec\Big\{\cot^{-1}\Big(-\frac{5}{12}\Big)\Big\}$

Find the general solutions of the following equations :

$\sin \theta=\frac{1}{2}$

Evaluate the following determinant:
$\begin{vmatrix}102&18&36\\1&3&4\\17&3&6\end{vmatrix}$

Let * be a binary operation defined by a * b = 3a + 4b − 2. Find 4 * 5.