Advertisements
Advertisements
प्रश्न
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
Advertisements
उत्तर
Let `I = int (x^3 sin (tan^-1 x^4))/(1 + x^8)` dx
Put tan-1 x4 = t
or `1/(1 + x^8) * 4x^3 dx = dt`
`1/(1 + x^8). x^3 = 1/4 dt`
Hence, `I = 1/4 int sin t dt`
`= - 1/4 cos t + C`
`= - 1/4 cos (tan^-1 x^4) + C`
APPEARS IN
संबंधित प्रश्न
Show that: `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Evaluate : `∫1/(3+2sinx+cosx)dx`
Solve:
dy/dx = cos(x + y)
Evaluate `int 1/(3+ 2 sinx + cosx) dx`
Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]
Write a value of\[\int \log_e x\ dx\].
Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
Evaluate: \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]
Evaluate : `int ("e"^"x" (1 + "x"))/("cos"^2("x""e"^"x"))"dx"`
Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`
Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`
Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`
Integrate the following functions w.r.t. x : `(1)/(sqrt(x) + sqrt(x^3)`
Integrate the following function w.r.t. x:
`(10x^9 +10^x.log10)/(10^x + x^10)`
Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sin x - cosx)dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Evaluate the following integrals:
`int (2x + 1)/(x^2 + 4x - 5).dx`
Integrate the following w.r.t.x: `(3x + 1)/sqrt(-2x^2 + x + 3)`
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
Evaluate the following.
`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
State whether the following statement is True or False.
If ∫ x f(x) dx = `("f"("x"))/2`, then find f(x) = `"e"^("x"^2)`
`int sin^-1 x`dx = ?
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
`int ("d"x)/(sinx cosx + 2cos^2x)` = ______.
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
Evaluate `int1/(x(x - 1))dx`
Evaluate:
`int 1/(1 + cosα . cosx)dx`
If f'(x) = 4x3- 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
`intx^3/sqrt(1 + x^4)dx`
