Final Answer
$-2\cos\left(\sqrt{x}\right)+C_0$
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Step-by-step Solution
Problem to solve:
$\int\frac{\sin\left(\sqrt{x}\right)}{\sqrt{x}}dx$
Specify the solving method
1
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.
$\int x^{-\frac{1}{2}}\sin\left(\sqrt{x}\right)dx$
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
$-2\cos\left(\sqrt{x}\right)+C_0$