Evaluate: 5 x+2 3 x-4 d x - Vidyadip

Question

Evaluate:
$\int \frac{5 x+2}{3 x-4} \cdot d x$

✓

Answer

$\int \frac{5 x+2}{3 x-4} d x$
$=\int \frac{\frac{5}{3}(3 x-4)+\frac{20}{3}+2}{3 x-4} d x$
$=\int \frac{\frac{5}{3}(3 x-4)+\frac{26}{3}}{3 x-4} d x$
$=\int\left[\frac{5}{3}+\frac{\left(\frac{26}{3}\right)}{3 x-4}\right] d x$
$=\frac{5}{3} \int 1 d x+\frac{26}{3} \int \frac{1}{3 x-4} d x$
$=\frac{5 x}{3}+\frac{26}{3} \cdot \frac{1}{3} \log |3 x-4|+c$
$=\frac{5 x}{3}+\frac{26}{9} \log |3 x-4|+c .$

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 Integration→Indefinite Integration — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

If $\bar{a}=3 \hat{i}-\hat{j}+4 \hat{k}, \bar{b}=2 \hat{i}+3 \hat{j}-\hat{k}$ and $\bar{c}=-5 \hat{i}+2 \hat{j}+3 \hat{k}$, then $\bar{a} \cdot(\bar{b} \times \bar{c})$ is $\qquad$

If A is a square matrix satisfying $A^T A = l$, write the value of $|A|$.

Answer the following quations in one word or one sentence or as per exact requirement of the question:
Write the distance of a point P(a, b, c) from x-axis.

If $x=\sin ^{-1}\left(e^t\right), y=\sqrt{1-e^{2 t}}$, show that $\sin x+\frac{d y}{d x}=0$

If $\int_{0}^\limits{\text{a}}3\text{x}^2\text{ dx}=8,$ find the value of a.

Which of the following distributions of a random variable X are the probability distributions?

X:	0	1	2	3
P(X):	0.3	0.2	0.4	0.1

Is * defined on the set {1, 2, 3, 4, 5} by a * b = LCM of a and b a binary operation? Justify your answer.

Divide the number 30 into two parts such that their product is maximum.

If, $\bar{a}=\hat{i}-2 \hat{j}, \bar{b}=\hat{i}+2 \hat{j}$ and $\bar{c}=2 \hat{i}+\hat{j}-2$ then find

(i) $\bar{a} \times(\bar{b} \times \bar{c})$

Find the angle between the vectora $\vec{\text{a}}=\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}}$ and $\vec{\text{b}}=\hat{\text{i}}+\hat{\text{j}}-\hat{\text{k}}.$