Advertisements
Advertisements
Question
Integrate the following with respect to x.
sin3x
Advertisements
Solution
sin3x = 3 sin x – 4sin3x
4sin3x = 3 sin x – sin3x
⇒ sin3x = `1/4 [3 sin x - sin^3x]`
`int sin^3x "d"x = 1/4 int (3 sin x - sin^3x) "d"x`
= `1/4 [3(- cos x) - ((- cos 3x)/2)] + "c"`
= `(-3)/4 [cos x] + 1/12 [cos 3x] + "c"`
APPEARS IN
RELATED QUESTIONS
Integrate the following with respect to x.
`1/(sqrt(x + 1) + sqrt(x - 1))`
Integrate the following with respect to x.
`(4x^2 + 2x + 6)/((x + 1)^2(x - 3))`
Integrate the following with respect to x.
`"e"^(xlog"a") + "e"^("a"log"a") - "e"^("n"logx)`
Integrate the following with respect to x.
xe–x
Integrate the following with respect to x.
`(2x + 5)/(x^2 + 5x - 7)`
Integrate the following with respect to x.
`1/(2x^2 - 9)`
Integrate the following with respect to x.
`1/sqrt(9x^2 - 7)`
Choose the correct alternative:
`int "e"^(2x) [2x^2 + 2x] "d"x`
Choose the correct alternative:
`int "e"^x/("e"^x + 1) "d"x` is
Evaluate the following integral:
`int ("d"x)/("e"^x + 6 + 5"e"^-x)`
