Evaluate x^2+4x x^3+6x^2+5 dx - Vidyadip

Question

Evaluate $\int\frac{\text{x}^2+4\text{x}}{\text{x}^3+6\text{x}^2+5}\text{ dx}$

✓

Answer

Let $\text{I}=\int\frac{\text{x}^2+4\text{x}}{\text{x}^3+6\text{x}^2+5}\text{ dx}$
Let $\text{x}^3+6\text{x}^2+5=\text{t}$
$(3\text{x}^2+12\text{x})\text{dx}=\text{dt}$
$3(\text{x}^2+4\text{x})\text{dx}=\text{dt}$
$\therefore\ \text{I}=\frac{1}{3}\int\frac{\text{dt}}{\text{t}}$
$=\frac{1}{3}\log\text{t}+\text{C}$
$\text{I}=\frac{1}{3}\log\big|\text{x}^3+6\text{x}^2+5\big|+\text{C}$

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

If $f(x)=2 x+5$ and $g(x)=x^2+1$ be two real functions, then describe the following functions:
gof
Also, show that fof $\neq f^2$

Prove that 1, 1, 1 cannot be direction cosines of a straight line.

If A is a square matrix of order $3$ such that |A| = 5, write the value of $|adj A|$.

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

Find the angle between the lines $\bar{r}=3 \hat{i}+2 \hat{j}-4 \widehat{k}+\lambda(\hat{i}+2 \hat{j}+2 \widehat{k})$ and $\bar{r}=5 \hat{i}-2 \widehat{k}+\mu(3 \hat{i}+2 \hat{j}+6 \widehat{k})$

Integrate the following functions w.r.t. x:

$\frac{\left(x^2+2\right)}{\left(x^2+1\right)} \cdot a^{x+\tan ^{-1} x}$

Show that equation $2 x^2-x y-3 y^2-6 x+19 y-20=0$ represents a pair of lines.

Diffrentiate the following w.r.t.x

$e^{3 \sin 2 x-2 \cos 2 x}$

If $\text{A}=\begin{bmatrix}\cos\text{x}&-\sin\text{x}\\\sin\text{x}&\cos\text{x}\end{bmatrix},$ find $AA^T$.

If $A=\left[\begin{array}{ll}2 & 0 \\ 0 & 1\end{array}\right]$ and $B=\left[\begin{array}{l}1 \\ 2\end{array}\right]$ then find the matrix $X$ such that $A^{-1} X=B$