How do you find the integral of $\frac{1}{x^{\frac{1}{2}}} sin (x^{\frac{1}{2}})$ $1/(x^(1/2))sin(x^(1/2))$ ?

Question

How do you find the integral of $\frac{1}{x^{\frac{1}{2}}} sin (x^{\frac{1}{2}})$ $1/(x^(1/2))sin(x^(1/2))$ ?

1 Answer

Impact of this question

4752 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-20T12:58:19

$\int \frac{1}{x^{\frac{1}{2}}} sin (x^{\frac{1}{2}}) d x = - 2 cos (x^{\frac{1}{2}}) + c$ $int1/x^(1/2)sin(x^(1/2))"d"x=-2cos(x^(1/2))+"c"$

Explanation:

Let $u = x^{\frac{1}{2}}$ $u=x^(1/2)$ and $d u = \frac{1}{2 x^{\frac{1}{2}}} d x$ $"d"u=1/(2x^(1/2))"d"x$ so $2 d u = \frac{1}{x^{\frac{1}{2}}} d x$ $2"d"u=1/(x^(1/2))"d"x$

Then

$\int \frac{1}{x^{\frac{1}{2}}} {sin x}^{\frac{1}{2}} d x = 2 \int sin u d u = - 2 cos u = - 2 {cos x}^{\frac{1}{2}} + c$ $int1/x^(1/2)sinx^(1/2)"d"x=2intsinu"d"u=-2cosu=-2cosx^(1/2)+"c"$

Science

Math

Humanities

... and beyond

How do you find the integral of $\frac{1}{x^{\frac{1}{2}}} sin (x^{\frac{1}{2}})$ $1/(x^(1/2))sin(x^(1/2))$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you find the integral of 1x12sin(x12)1/(x^(1/2))sin(x^(1/2))?

1 Answer

Explanation:

Related questions

Impact of this question

How do you find the integral of $\frac{1}{x^{\frac{1}{2}}} sin (x^{\frac{1}{2}})$ $1/(x^(1/2))sin(x^(1/2))$ ?