Integrate the functions in Exercises: 3x^2 x^6+1 - Vidyadip

Question

Integrate the functions in Exercises:
$\frac{3\text{x}^2}{\text{x}^6+1}$

✓

Answer

$\text{Let I}=\int\frac{3\text{x}^2}{\text{x}^6+1}\text{ dx}$
$=\int\frac{3\text{x}^2}{(\text{x}^3)^2+1}\text{ dx} \ \ \ \ \ ...\text{(i)}$
Putting$\ \ \ \text{x}^3=\text{t} \ \ \ \ \ \ \ \Rightarrow \ \ \ \ \ \ \ 3\text{x}^2=\frac{\text{dt}}{\text{dx}} \ \ \ \ \ \ \Rightarrow \ \ \ \ \ \ \ 3\text{x}^2\text{ dx}=\text{dt}$
$\therefore \ \ \ \ \ $From eq. (i),$\ \ \ \ \text{I}=\int\frac{\text{dt}}{\text{t}^2+1}=\frac{1}{1}\tan^{-1}\frac{\text{t}}{1}+\text{c}$
$=\tan^{-1}\text{x}^3+\text{c}$

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 "2 Marks Questions" 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

If P, Q and R are three collinear points such that $\overrightarrow{\text{PQ}}=\vec{\text{a}}\text{ and }\overrightarrow{\text{QR}}=\vec{\text{b}}$. Find the vector $\overrightarrow{\text{PR}}$.

If the area of a triangle is 18 sq units and vertices are $(x, 7) ;(2,2)$ and $(10,8)$, then find the value of $x$.

Write the value of the determinant $\begin{vmatrix}\text{a}&1&\text{b}+\text{c}\\\text{b}&1&\text{c}+\text{a}\\\text{c}&1&\text{a}+\text{b}\end{vmatrix}$

Write the vector equation of a line passing through a point having position vector $\vec{\alpha}$ and parallel to vector $\vec{\beta}.$

f: Z → Z given by $f(x) = x^2$

Given $\text{A}=\begin{bmatrix}2 & -3 \\-4 & 7 \end{bmatrix},$ compute $A^{-1}$ and show that $2A^{-1} = 9I – A$.

If $\begin{bmatrix}\text{x}&2\end{bmatrix}\begin{bmatrix}3\\4\end{bmatrix}=2,$ find x.

An insurance company insured $2000$ scooter drivers, $4000$ car drivers and $6000$ truck drivers. The probability of an accidents are $0.01, 0.03$ and $0.15$ respectively. One of the insured persons meet with an accident. What is the probability that he is a scooter driver?

Let E and F be events with P (E) = $\frac{3}{5}$, P (F) = $\frac{3}{{10}}$ and $P(E \cap F)$ = $\frac{1}{5}$. Are E and F independent?

Find a matrix X such that 2A + B + X = 0, where.
$\text{A}=\begin{bmatrix}-1&2\\3&4\end{bmatrix},\text{B}=\begin{bmatrix}3&-2\\1&5\end{bmatrix}$