Advertisements
Advertisements
Question
Integrate the following functions w.r.t. x : `3^(cos^2x) sin 2x`
Advertisements
Solution
let I = `int 3^(cos^2x) sin2x dx`
Put cos2x = t
∴ `[2 cos x d/dx (cos x)]dx` = dt
∴ – 2 sin x cos x dx = dt
∴ sin 2x dx = – dt
I = `- int3^t dt`
= `-(1)/(log3).3^t + c`
= `-(1)/(log3).3^(cos^2x) + c`.
APPEARS IN
RELATED QUESTIONS
Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`
Show that: `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`
Integrate the functions:
`xsqrt(x + 2)`
Integrate the functions:
`(x^3 - 1)^(1/3) x^5`
Integrate the functions:
`x/(9 - 4x^2)`
Integrate the functions:
`sqrt(tanx)/(sinxcos x)`
Evaluate: `int (2y^2)/(y^2 + 4)dx`
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
\[\int\frac{\sin x + 2 \cos x}{2 \sin x + \cos x} \text{ dx }\]
`int "dx"/(9"x"^2 + 1)= ______. `
Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`
Integrate the following functions w.r.t. x : sin4x.cos3x
Integrate the following function w.r.t. x:
x9.sec2(x10)
Integrate the following functions w.r.t. x : `(x^n - 1)/sqrt(1 + 4x^n)`
Integrate the following functions w.r.t. x:
`x^5sqrt(a^2 + x^2)`
Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sin x - cosx)dx`
Evaluate the following integrals : `int (2x + 3)/(2x^2 + 3x - 1).dx`
Evaluate the following integral:
`int (3cosx)/(4sin^2x + 4sinx - 1).dx`
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
Evaluate the following.
`int 1/(sqrt(3"x"^2 - 5))` dx
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
Evaluate `int 1/((2"x" + 3))` dx
Evaluate: `int "e"^sqrt"x"` dx
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
`int x^2/sqrt(1 - x^6)` dx = ________________
`int (log x)/(log ex)^2` dx = _________
`int ("e"^x(x - 1))/(x^2) "d"x` = ______
`int x^x (1 + logx) "d"x`
State whether the following statement is True or False:
`int sqrt(1 + x^2) *x "d"x = 1/3(1 + x^2)^(3/2) + "c"`
Evaluate `int(3x^2 - 5)^2 "d"x`
`int (x^2 + 1)/(x^4 - x^2 + 1)`dx = ?
If f'(x) = `x + 1/x`, then f(x) is ______.
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
Evaluate `int(1 + x + x^2/(2!) )dx`
Evaluate `int (1+x+x^2/(2!))dx`
Solve the following Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3)dx`
`int x^3 e^(x^2) dx`
Evaluate.
`int (5x^2 - 6x + 3)/(2x - 3) dx`
`int x^2/sqrt(1 - x^6)dx` = ______.
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate the following.
`int 1/ (x^2 + 4x - 5) dx`
Evaluate `int(5x^2-6x+3)/(2x-3)dx`
Evaluate `int1/(x(x - 1))dx`
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
