Verify the following: 2x+3 x^2+3x dx= |x^2+3x |+c - Vidyadip

Question

Verify the following:
$\int\frac{2\text{x}+3}{\text{x}^2+3\text{x}}\text{dx}=\log\big|\text{x}^2+3\text{x}\big|+\text{c}$

✓

Answer

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

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 "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

Form the differential equation from the following primitives where constants are arbitrart:$\text{y}=\text{cx}+2\text{c}^2+\text{c}$

Differentiate w.r.t. x the function in Exercise:
$(3\text{x}^2-9\text{x}+5)^9$

Examine the consistency of the system of equation x + 2y = 2; 2x + 3y = 3

Show that the function f given by $f(x) = \tan^{–1} (sin\ x + cos\ x)$ is decreasing for all $\text{x} \in \bigg(\frac{\pi}{4}, \frac{\pi}{2}\bigg).$

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

Integrate the function: $x \sqrt{x+2}$

Write the value of $\lambda$ so that vectora $\vec{\text{a}}=2\hat{\text{i}}+\lambda\hat{\text{j}}+\hat{\text{k}}$ and $\vec{\text{b}}=\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}}$ are perpendicular to each other.

If $\text{f(x)}=\begin{cases}\frac{\text{x}}{\sin3\text{x}},&\text{x}\neq0\\\text{k},&\text{x}=0\end{cases}$ is continuous at x = 0, then write the value of k.

Let $\text{A}=\begin{bmatrix}2&4\\3&2\end{bmatrix},\text{B}=\begin{bmatrix}1&3\\-2&5\end{bmatrix}$ and $\text{C}=\begin{bmatrix}-2&5\\3&4\end{bmatrix}.$ Find each of the following:
$3\text{A}-2\text{B}+3\text{C}$

Find $\frac{d y}{d x}$, if $x^{\frac{2}{3}}+y^{\frac{2}{3}}=a^{\frac{2}{3}}$.