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Answer :

`(a^(x))/(log a) [x-(1)/(log a) ]+c`Transcript

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00:00 - 00:59 | head the given question evaluate the integral X into DX to go to solve this question let's use by parts formula what is bypass for it is used to integrate the two function in product so its integration is given by first function as it is integration of s function - integration of integration differentiation of first function into integration of second function and its whole integration with respect to explore this is the this is the by parts formula so here consider consider here XNXX first function and a to the power x s function to by using this by parts formula I can write are integral first function as it is to write activities and integration of e to the power x 3 x minus integration of cotx differentiation of x is one and integration |

01:00 - 01:59 | integration of DX and it again integration with respect to act so here are I become equal to X into integration of e to the power x to the power x divided by minus Navya integration of their integration of UV protected access to the power x / Allah ne so again its integration to hair I become equal to X X / LN a minus 1 by Alan a into it is integration is a to the power x divided by Alan A Plus TV Season 8 grating constant so finally I can write are integral and x to the power x divided by Alan - 8 x divided by Alan a and b whole square + c so this is the answer for the above integral |

**A function `phi(x)` is called a primitive of `f(x)`; if `phi'(x) = f(x)`**

**Some important formulas of integration**

**Examples of integration: (i) `x^4` (ii) `3^x`**

**Theorem: `d/dx(int f(x) dx) = f(x)`**

**The integral of the product of a constant and a function = the constant x integral of function**

**`int {f(x) pm g(x)} dx = int f(x) dx pm int g(x) dx`**

**Geometrical interpretation of indefinite integral**

**Comparison between differentiation and integration**

**By substitution: Theorem: If `int f(x) dx = phi(x)` then `int f(ax+b) dx = 1/a phi(ax + b)dx`**

**Examples: `1/ (cos3x+1) dx` and `1/((sqrt (x+a) + sqrt (x+b))) dx`**