Advertisements
Advertisements
प्रश्न
Evaluate of the following integral:
उत्तर
\[\int 3^{2 \log_{3^x}} dx\]
\[ = \int 3\log_3 x^2 dx\]
\[ = \int x^2 dx\]
\[ = \frac{x^3}{3} + C\]
APPEARS IN
संबंधित प्रश्न
Evaluate `int_(-1)^2|x^3-x|dx`
Evaluate :
`∫_(-pi)^pi (cos ax−sin bx)^2 dx`
find `∫_2^4 x/(x^2 + 1)dx`
Evaluate :
`∫_0^π(4x sin x)/(1+cos^2 x) dx`
Evaluate :
`int_e^(e^2) dx/(xlogx)`
Evaluate: `intsinsqrtx/sqrtxdx`
Evaluate the integral by using substitution.
`int_0^1 sin^(-1) ((2x)/(1+ x^2)) dx`
Evaluate the integral by using substitution.
`int_0^2 xsqrt(x+2)` (Put x + 2 = `t^2`)
Evaluate the integral by using substitution.
`int_(-1)^1 dx/(x^2 + 2x + 5)`
Evaluate `int_0^(pi/4) (sinx + cosx)/(16 + 9sin2x) dx`
Evaluate:
Evaluate :
Evaluate:
Evaluate the following definite integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate each of the following integral:
Evaluate each of the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate : \[\int\limits_{- 2}^1 \left| x^3 - x \right|dx\] .
Find : \[\int e^{2x} \sin \left( 3x + 1 \right) dx\] .
Evaluate: \[\int\limits_0^{\pi/2} \frac{x \sin x \cos x}{\sin^4 x + \cos^4 x}dx\] .
Evaluate: `int_-1^2 (|"x"|)/"x"d"x"`.
Find: `int_ (3"x"+ 5)sqrt(5 + 4"x"-2"x"^2)d"x"`.
Evaluate the following:
`int "dt"/sqrt(3"t" - 2"t"^2)`
Find: `int (dx)/sqrt(3 - 2x - x^2)`
Evaluate: `int_0^(π/2) sin 2x tan^-1 (sin x) dx`.
Evaluate: `int x/(x^2 + 1)"d"x`
Evaluate:
`int (1 + cosx)/(sin^2x)dx`
If `int x^5 cos (x^6)"d"x = "k" sin (x^6) + "C"`, find the value of k.