Find the integral: x ( x + x ) d x. - Vidyadip

Question

Find the integral: $\int \sec x ( \sec x + \tan x ) d x.$

✓

Answer

Let I = $\int \sec x ( \sec x + \tan x ) d x$
$= \int \left( \sec ^ { 2 } x + \sec x \tan x \right) d x$
$= \int \sec ^ { 2 } x d x + \int \sec x \tan x d x$
= tan x + secx + 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

Write the value of $\cot^{-1}(-\text{x})$ for all $\text{x}\in\text{R}$ in terms of $\cot^{-1}\text{x}$

If y = x|x|, find $\frac{\text{dy}}{\text{dx}}\text{ for x 0}<0.$

Let $R = \{(a, a^3):$ a is a prime number less than $5\}$ be a relation. Find the range of $R.$

If $A$ and $B$ are square matrices of the same order, explain, why in general:
$(A − B)^2 \neq A^2 − 2AB + B^2$

The Cartesian equation of a line is $\frac{{x - 5}}{3} = \frac{{y + 4}}{7} = \frac{{z - 6}}{2}$. Write its vector form.

Define continuity of a function at a point.

Evaluate the following integrals:$\int\text{x}^{\text{n}}.\log\text{x dx}$

Evaluate the following integrals:
$\int\bigg (2^{\text{x}}+\frac{5}{\text{x}}-\frac{1}{\text{x}^{\frac{1}{3}}}\bigg)\text{dx}$

Assume that each child born is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that,

The youngest is a girl.
At least one is a girl?

Evaluate the following integrals:
$\int\frac{1}{1+\cos2\text{x}}\text{dx}$