Integrate the function 3 x^ 2 x^ 6 +1 - Vidyadip

Question

Integrate the function $\frac{3 x^{2}}{x^{6}+1}$

✓

Answer

Let x³ = t
$\Rightarrow$ 3x² dx = dt
$\Rightarrow \int \frac{3 x^{2}}{x^{6}+1} d x=\int \frac{d t}{t^{2}+1}$
= tan^-1t + C
= tan^-1(x³) + 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 "2 Marks" from Integrals→Integrals — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Find the value of k so that the lines x = -y = kz and x - 2 = 2y + 1 = -z + 1 are perpendicular to each other.

A bag contains 2 white, 3 red and 4 blue balls. Two balls are drawn at random from the bag. If X denotes the number of white balls among the two balls drawn, describe the probability distribution of X.

If A is a non-singular square matrix such that |A| = 10, find |A^-1|.

Evaluate the following integrals:
$\int\frac{\text{e}^\text{x}}{(1+\text{e}^\text{x})^2}\text{dx}$

Find the interval where function $f(x)=x^3-3 x$ is decreasing.

Evalute the following integrals:
$\int\frac{\text{e}^{3\text{x}}}{\text{e}^{3\text{x}}+1}\text{dx}$

Three cards are drawn with replacement from a well shuffled pack of cards. Find the probability that the cards drawn are king, queen and jack.

Two cards are drawn without replacement from a pack of 52 cards. Find the probability that.
Both are kings.

If A = {1, 2, 3, 4} and B = {a, b, c, d} define any four bijections from A to B. Also give their inverse functions.

Discuss the applicability of the Rolle's theorem for the following function on the indicated interval
$\text{f}(\text{x})=2\text{x}^2-5\text{x}+3\text{ on }[1,3]$