Evaluate the following integrals: ^3 2 x ^2x dx - Vidyadip

Question

Evaluate the following integrals:
$\int\tan^\frac{3}{2}\text{x}\sec^2\text{x dx}$

✓

Answer

$\int\tan^\frac{3}{2}\text{x}\sec^2\text{x dx}$
$\text{Let, }\tan\text{x}=\text{t}$
$\Rightarrow\sec^2\text{x}=\frac{\text{dt}}{\text{dx}}$
$\Rightarrow\sec^2\text{x dx}=\text{dt}$
$\text{Now,}\int\tan^\frac{3}{2}\text{x}\sec^2\text{x dx}$
$=\int\text{t}^\frac{3}{2}\text{dt}$
$=\Bigg[\frac{\text{t}^{\frac{3}{2}+1}}{\frac{3}{2}+1}\Bigg]+\text{C}$
$=\frac{2}{5}\text{t}^\frac{5}{2}+\text{C}$
$=\frac{2}{5}\tan^\frac{5}{2}\text{x}+\text{C}$

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" 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

If e^x+y - x = 0, prove that $\frac{\text{dy}}{\text{dx}}=\frac{1-\text{x}}{\text{x}}$

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

Write a value of $\int\text{e}^{\text{x}}\Big(\frac{1}{\text{x}}-\frac{1}{\text{x}^2}\Big)\text{dx}$

If the matric $\text{A}=\begin{bmatrix}5 & 2&\text{x} \\\text{y} & \text{z}&-3\\4&\text{t}&-7\end{bmatrix}$ is a symmetric matrix, find x, y, z and t.

Find the general solution of the differential equation $x \frac{d y}{d x}+2 y=x^{2}(x \neq 0)$

If $\text{A}=\begin{bmatrix}1&2\\0&3 \end{bmatrix}$ is written as B + C, where B is a symmetric matrix and C is a skew- symmetric matrix, then B is equal to.

The probability of a man hitting a target is 1/4. If he fires 7 times, what is the probability of his hitting the target at least twice?

Without using the derivative show that the function f(x) = 7x - 3 is strictly increasing function on R.

An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random. What is the probability that the second ball is red?

Show that the line joining the origin to the points (2, 1, 1) is perpendicular to the line detarmined by the points (3, 5, -1) and (4, 3, -1).