إيجاد تكامل غير محدد
MathematicsCalculus (Integrals)Medium
Published:
Question
$$\int (1 + \tan x) dx$$
Animated Video Solution
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Step by Step Written Solution
1
Step 1
Hi Ahmed, let's solve this integration problem together. We need to find the integral of one plus x plus tan squared of x with respect to x.
حل التكامل
$$\int(1 + x + \tan^2 x) dx$$
2
Step 2
To make this easier, we can recall a fundamental trigonometric identity.
متطابقة مثلثية:
3
Step 3
We know that one plus tan squared of x equals secant squared of x. Let's write that down.
$$1 + \tan^2 x = \sec^2 x$$
4
Step 4
Now, let's look at our integral again and regroup the terms to use this identity.
5
Step 5
We replace one plus tan squared with secant squared.
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