Solve \int \frac{cos \sqrt{t}}{\sqrt{t}} d t

Evaluate

\int \frac{cos ( t )}{t} d t

Rewrite the expression

\int \frac{cos ( t ^{\frac{1}{2}} )}{t ^{\frac{1}{2}}} d t

Use the substitution d t = 2 t^{\frac{1}{2}} d v to transform the integral

More Steps

\int \frac{cos ( t ^{\frac{1}{2}} )}{t ^{\frac{1}{2}}} \times 2 t^{\frac{1}{2}} d v

Simplify

More Steps

\int 2 cos (t^{\frac{1}{2}}) d v

Use the substitution v = t^{\frac{1}{2}} to transform the integral

\int 2 cos (v) d v

Use the property of integral \int k f (x) d x = k \int f (x) d x

2 \times \int cos (v) d v

Use the property of integral \int cos (x) d x = sin (x)

2 sin (v)

Substitute back

2 sin (t^{\frac{1}{2}})

Use a^{\frac{m}{n}} = n a^{m} to transform the expression

2 sin (t)

Solution

2 sin (t) + C, C \in R

Evaluate the integral