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

Question

$\int\frac{1}{2-3\text{x}}+\frac{1}{\sqrt{3\text{x}-2}}\text{dx}$

✓

Answer

$\int\Big(\frac{1}{2-3\text{x}}+\frac{1}{\sqrt{3\text{x}-2}}\Big)\text{dx}$
$=\int\frac{\text{dx}}{2-3\text{x}}+\int(3\text{x}-2)^{-\frac{1}{2}}\text{dx}$
$=\frac{\ln(2-3\text{x})}{-3}+\Bigg[\frac{(3\text{x}-2)^{-\frac1{2}+1}}{3\big(-\frac{1}{2}+1\big)}\Bigg]+\text{c}$
$=\frac{\ln(2-3\text{x})}{-3}+\frac{2}{3}(3\text{x}-2)^{\frac{1}{2}}+\text{c}$
$=-\frac{1}{3}\ln(2-3\text{x})+\frac{2}{3}\sqrt{3\text{x}-2}+\text{c}$

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 "3 Marks Question" 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

Evaluate the following integrals:
$\int\frac{(\text{x}+1)\text{e}^\text{x}}{\cos^2(\text{xe}^\text{x})}\text{ dx}$

Evaluate the following definite integrals:
$\int_{0}^\limits{2\pi}\text{e}^{\text{x}}\cos\Big(\frac{\pi}{4}+\frac{\text{x}}{2}\Big)\text{dx}$

Evaluate the following integrals:
$\int\limits^\frac{\pi}{2}_{-\frac{\pi}{2}}\sin^3\text{x}\text{ dx}$

Given A = {2, 3, 4}, B = {2, 5, 6, 7}. Construct an example of each of the following:

An injective map from A to B.
A mapping from A to B which is not injective.
A mapping from A to B.

Of the students in a college, it is known that $60\%$ reside in hostel and $40\%$ are day scholars (not residing in hostel). Previous year results report that $30\%$ of all students who reside in hostel attain. A grade and $20\%$ of day scholars attain A grade in their annual examination. At the end of year, one student is chosen at random from the college and he has an A grade, what is the probability that the student is a hostlier?

Find the slope of the normal at the point 't' on the curve $\text{x}=\frac{1}{\text{t}},\text{y}=\text{t}.$

Integrate the function in Exercise:
$\frac{1}{\text{x}\sqrt{\text{ax}-\text{x}^{2}}}$
$\big[\text{Hint:putx}=\frac{\text{a}}{\text{t}}\big]$

Evaluate the following integrals:
$\int\frac{1}{1-\sin\text{x}}\text{dx}$

State with reasons whether the following functions have inverse:
f : {1, 2, 3, 4} → {10} with f = {(1, 10), (2, 10), (3, 10), (4, 10)}

Differentiate the following functions with respect to x:
$\log(\cos\text{x}^2)$