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

The integral of (7cos(sqrt(x))) is 14(sqrt(x)sin(sqrt(x))+cos(sqrt(x)))+C

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integral of (7cos(sqrt(x)))

\int (7 cos (x)) d x

14 (x sin (x) + cos (x)) + C

Solution steps

\int 7 cos (x) d x

Take the constant out:

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

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

Apply u-substitution

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

= 7 \cdot \int cos (u) \cdot 2 u d u

Take the constant out:

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

= 7 \cdot 2 \cdot \int cos (u) u d u

Apply Integration By Parts

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

= 7 \cdot 2 (u sin (u) - \int sin (u) d u)

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

= 7 \cdot 2 (u sin (u) - (- cos (u)))

Substitute back

u = x

= 7 \cdot 2 (x sin (x) - (- cos (x)))

Simplify

= 14 (x sin (x) + cos (x))

Add a constant to the solution

= 14 (x sin (x) + cos (x)) + C

x \to 0 lim (\frac{( x + 2 ) ^{3} - 8}{x})

\frac{\partial}{\partial x} (ln (1 + x^{2} + y^{2} + z^{2}))

f (x) = (1 + 2 x^{2}) (x - x^{2})

\int_{0}^{5} 2 π (6 - x) (25 - x^{2}) d x

arcsin (cos (x^{6}))

What is the integral of (7cos(sqrt(x))) ?
The integral of (7cos(sqrt(x))) is 14(sqrt(x)sin(sqrt(x))+cos(sqrt(x)))+C