integrate the following
Answers
Answer:
1
------------ sin⁻¹ (aˣ) + c
log a
e
Step-by-step explanation:
To find--->
-----------
aˣ
∫------------------dx
√ (1-a²ˣ)
Solution--->
-------------
let
aˣ
I= ∫-------------------dx
√{(1) - (aˣ)²}
let
aˣ= t
differentiating with respect to x
aˣ log a dx = dt
e
dt
aˣ dx = --------
log a
e
1 dt
I= ∫---------------- ---------
√(1 - t²) log a
e
1 1
= -------- ∫ ----------- dt
log a √(1-t²)
e
1
=----------- sin⁻¹ t +c
log a
e
1
= ----------- sin⁻¹ (aˣ) + c
log a
e
additional information--->
------------------------------------
1 x
1: ∫--------------dx = sin⁻¹(------) + c
√a² -x² a
1 1 x
2: ∫---------------dx= ------ tan⁻¹(--------)+c
a² + x² a a
1 1 x
3:∫---------------------dx =-------sec⁻¹ (-----)+c
x √x²- a² a a
Hope it helps u
Thanks