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Integrate $\int\frac{\sin\left(\sqrt{x}\right)}{\sqrt{x}}dx$

Step-by-step Solution

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Final Answer

$-2\cos\left(\sqrt{x}\right)+C_0$
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Step-by-step Solution

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Rewrite the exponent using the power rule $\frac{a^m}{a^n}=a^{m-n}$, where in this case $m=0$

$\int x^{-\frac{1}{2}}\sin\left(\sqrt{x}\right)dx$

Learn how to solve integrals with radicals problems step by step online.

$\int x^{-\frac{1}{2}}\sin\left(\sqrt{x}\right)dx$

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Learn how to solve integrals with radicals problems step by step online. Integrate int(sin(x^1/2)/(x^1/2))dx. Rewrite the exponent using the power rule \frac{a^m}{a^n}=a^{m-n}, where in this case m=0. We can solve the integral \int x^{-\frac{1}{2}}\sin\left(\sqrt{x}\right)dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify u and calculate du. Now, identify dv and calculate v.

Final Answer

$-2\cos\left(\sqrt{x}\right)+C_0$

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve integral of (sin(x^0.5)/(x^0.5))dx using basic integralsSolve integral of (sin(x^0.5)/(x^0.5))dx using u-substitutionSolve integral of (sin(x^0.5)/(x^0.5))dx using integration by partsSolve integral of (sin(x^0.5)/(x^0.5))dx using tabular integration

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1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

Main Topic: Integrals with Radicals

Integrals with radicals are those integrals that contain a radical (square root, cubic, etc.) in the numerator or denominator of the integral.

Used Formulas

8. See formulas

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