What is the integral of 3cos(sqrt(7x)) ?

The integral of 3cos(sqrt(7x)) is 6/7 (sqrt(7)sqrt(x)sin(sqrt(7)sqrt(x))+cos(sqrt(7)sqrt(x)))+C

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integral of 3cos(sqrt(7x))

\int 3 cos (7 x) d x

\frac{6}{7} (7 x sin (7 x) + cos (7 x)) + C

Solution steps

\int 3 cos (7 x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int cos (7 x) d x

Apply u-substitution

: \int cos (u) \frac{1}{7} d u

= 3 \cdot \int cos (u) \frac{1}{7} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \frac{1}{7} \cdot \int cos (u) d u

Apply u-substitution

: \int cos (v) \cdot 2 v d v

= 3 \cdot \frac{1}{7} \cdot \int cos (v) \cdot 2 v d v

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \frac{1}{7} \cdot 2 \cdot \int cos (v) v d v

Apply Integration By Parts

: v sin (v) - \int sin (v) d v

= 3 \cdot \frac{1}{7} \cdot 2 (v sin (v) - \int sin (v) d v)

\int sin (v) d v = - cos (v)

= 3 \cdot \frac{1}{7} \cdot 2 (v sin (v) - (- cos (v)))

Substitute back

= 3 \cdot \frac{1}{7} \cdot 2 (7 x sin (7 x) - (- cos (7 x)))

Simplify

3 \cdot \frac{1}{7} \cdot 2 (7 x sin (7 x) - (- cos (7 x))) : \frac{6}{7} (7 x sin (7 x) + cos (7 x))

= \frac{6}{7} (7 x sin (7 x) + cos (7 x))

Add a constant to the solution

= \frac{6}{7} (7 x sin (7 x) + cos (7 x)) + C

y^{^{''}} + 49 y^{^{'}} = 0

\frac{\partial}{\partial a} (cos (a) sin (a + 2 b))

\frac{\partial}{\partial x} (3 x^{2} - 2 x y + y^{2} - 8 y)

x \to \infty lim (x + x - x - x)

x \to 2 lim (x^{3} - 1)

What is the integral of 3cos(sqrt(7x)) ?
The integral of 3cos(sqrt(7x)) is 6/7 (sqrt(7)sqrt(x)sin(sqrt(7)sqrt(x))+cos(sqrt(7)sqrt(x)))+C