Advertisements
Advertisements
Question
Advertisements
Solution
Let I= \[\int\]sin3 x . cos x dx
⇒ cos x dx = dt
\[ = \frac{\sin^4 x}{4} + C \left( \because t = \sin x \right)\]
APPEARS IN
RELATED QUESTIONS
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Evaluate : `∫1/(cos^4x+sin^4x)dx`
Evaluate :
`int1/(sin^4x+sin^2xcos^2x+cos^4x)dx`
Integrate the functions:
`(1+ log x)^2/x`
`(10x^9 + 10^x log_e 10)/(x^10 + 10^x) dx` equals:
Evaluate : `∫1/(3+2sinx+cosx)dx`
Evaluate: `int (sec x)/(1 + cosec x) dx`
Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Evaluate the following integrals:
`int x/(x + 2).dx`
If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`
Integrate the following function w.r.t. x:
`(10x^9 +10^x.log10)/(10^x + x^10)`
Integrate the following functions w.r.t.x:
`(5 - 3x)(2 - 3x)^(-1/2)`
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Evaluate the following integrals : `int (3x + 4)/sqrt(2x^2 + 2x + 1).dx`
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
Integrate the following w.r.t.x: `(3x + 1)/sqrt(-2x^2 + x + 3)`
Evaluate the following.
`int "x"^5/("x"^2 + 1)`dx
Evaluate the following.
`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx
`int sqrt(1 + "x"^2) "dx"` =
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
`int x^2/sqrt(1 - x^6)` dx = ________________
`int (sin4x)/(cos 2x) "d"x`
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int(1 - x)^(-2) dx` = ______.
State whether the following statement is True or False:
If `int x "f"(x) "d"x = ("f"(x))/2`, then f(x) = `"e"^(x^2)`
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
If `int x^3"e"^(x^2) "d"x = "e"^(x^2)/2 "f"(x) + "c"`, then f(x) = ______.
`int (f^'(x))/(f(x))dx` = ______ + c.
Evaluate the following.
`int x^3/(sqrt(1+x^4))dx`
Evaluate the following.
`int x^3 e^(x^2) dx`
The value of `int ("d"x)/(sqrt(1 - x))` is ______.
Evaluate the following:
`int (1) / (x^2 + 4x - 5) dx`
Evaluate `int1/(x(x-1))dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4)dx`
Evaluate the following:
`int x^3/(sqrt(1 + x^4)) dx`
