Evaluate x^2 1+x^3 dx - Vidyadip

Question

Evaluate $\int\frac{\text{x}^2}{1+\text{x}^3}\text{ dx}$

✓

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 "2 Marks" from Indefinite Integrals→Indefinite 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 f is an integrable function, show that:
$\int\limits^{\text{a}}_{-\text{a}}\text{f}\big(\text{x}^2\big)\text{dx}=2\int\limits^\text{a}_0\text{f}\big(\text{x}^2\big)\text{dx}$

Find the equation of the plane passing through the following point:
(1, 1, 1), (1, -1, 2) and (-2, -2, 2)

For any two vectors $\vec{\text{a}}$ and $\vec{\text{b}},$ find $\vec{\text{a}}.\big(\vec{\text{b}}\times\vec{\text{a}}\big).$

Find the area of the smaller part of the circle $x^2+y^2=a^2$ cut off by the line $x=\frac{a}{\sqrt{2}}$.

Find the equation of the plane passing through the following point:
(2, 3, 4), (-3, 5, 1) and (4, -1, 2)

Let f : R → R and g : R → R be defined by f(x) = x² and g(x) = x + 1. Show that fog ≠ gof.

Evaluate the following integrals:
$\int\limits^1_0\text{xe}^{\text{x}^2}\text{dx}$

If A = [A_ij] is a 3 × 3 scalar matrix such that a₁₁ = 2, then write the value of |A|.

If function $F (x)=\frac{\sin (10 x)}{x}, x \neq 0$, is continuous at $x=0$. Then find the value of $F (0)$.

If $A=\left[\begin{array}{cc}2 & 3 \\ 1 & -4\end{array}\right]$ and $B=\left[\begin{array}{cc}1 & -2 \\ -1 & 3\end{array}\right]$ then verify that $(A B)^{-1}=B^{-1} A^{-1}$