Question

12) a) Evaluate, integrate x^2Tan-1x.dx​

Answer 1

Answer:

$\star \boxed{\bold{ \frac{ {x}^{3} }{3} { \tan}^{ - 1} x - \frac{1}{6} (1 + {x}^{2} - log |1 + {x}^{2} | ) + c}}$

Here , In this question :

• We use integration by parts ,the formula is :

$\star \boxed{ \red{\bold{ \int \: uv \: dx = u \int \: v \: dx - \int \: ( \frac{du}{dx} \int \: v \: dx)dx}}}$

The above formula can be stated as :

• The integral product of two functions

= first function u multiplied by integral of 2nd function v

- integral of ( d.c of 1st function multiplied by integral

of 2nd function) .

Solution refer to the attachment

Answer 2

Step-by-step explanation:

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