Top 100 Integration Q&A

, Calculus
Top 100 Integration Q&A
1) 𝒙

Solution
sin 𝑥

∫ 𝑑𝑥

− ∫ 𝑑𝑥 − cos 𝑥




cos 𝑥

∫ 𝑑𝑥

− ∫ 𝑑𝑥 sin 𝑥




∗ ∗

∗ ∗


𝟏
2)
𝟏 𝐜𝐨𝐬 𝒙

Solution

, As

Thus = =
∗ ∗

= =
𝒄𝒐𝒔𝟐 (𝟐𝒙 𝟑)
3)
𝟏 𝐬𝐢𝐧(𝟐𝒙 𝟑)

Solution
( ) ( )
=
( ) ( )
( ( ))∗( ( ))
= =
( )

=
𝒄𝒐𝒔𝟑 𝒙 𝐜𝐨𝐬 𝒙
4)
𝒔𝒊𝒏𝟐 𝒙 𝟐𝒄𝒐𝒔𝟐 𝒙

Solution
( )
=
( )

= = =
𝐜𝐨𝐬 𝒙
5)
𝟏 𝒄𝒐𝒔𝟐 𝒙

Solution
= =

=

, 𝒅𝒙
6)
𝟏 𝒄𝒐𝒔𝟐 𝒙

Solution

= = =
𝟔
7) 𝟐 𝟑


Solution
2
Let Thus 𝑑
( )
= =
( )
=

8) 𝟑 𝟒 𝟓

Solution
=

( )
As =
Thus
( )
=
( )
=
𝒙 𝟑
9)
(𝒙𝟐 𝟔𝒙)𝟕