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

Question

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

✓

Answer

Let $\text{I}=\int\frac{\text{x}^2}{1+\text{x}^2}\text{ dx}$
Let $1+\text{x}^3=\text{t}$
$3\text{x}^2\text{dx}=\text{dt}$
$\text{x}^2\text{dx}=\frac{1}{3}\text{dt}$
$\therefore\ \frac{1}{3}\int\frac{\text{dt}}{\text{t}}=\frac{1}{3}\log\text{t}+\text{C}$
$\text{I}=\frac{1}{3}\log|1+\text{x}^3|+\text{C}$

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

Diffrentiate the following w.r.t.x

$\log _{e^2}(\log x)$

Find the volume of a parallelopiped whose coterminus edges are represented by the

vector $\hat{j}+\hat{k} \cdot \hat{i}+\hat{k}$ and $\hat{i}+\hat{j}$. Also find volume of tetrahedron having these

coterminous edges.

The binary operation *: R × R → R is defined as a * b = 2a + b. Find (2 * 3) * 4.

Find k if, the sum of the slopes of the lines represented by $x^2+k x y-3 y^2=0$ is twice their product.

Evaluate the following:

$\int \cos (\sqrt[3]{x}) d x$

Show that the following systems of linear equations has infinite number of solutions and solve:

Draw the graph of inequalities $x ≤ 6, y −2 ≤ 0, x ≥ 0, y ≥ 0$ and indicate the feasible region

If $y=\cos ^{-1}\left(1-2 \sin ^2 x\right)$, find $\frac{d y}{d x}$

Write the identity element for the binary operation * on the set $R _0$ of all non-zero real numbers by the rule $a \times b=\frac{a b}{2}$ for all $a, b \in R_0$.

Let * be a binary operation on Q - {-1} defined by a * b = a + b + ab for all a, b ∈ Q - {-1}. Then,
Find the identity element in Q − {−1}.