Integral of sin(4x+3) dx

The solution

You have entered [src]

  1                
  /                
 |                 
 |  sin(4*x + 3) dx
 |                 
/                  
0

$$\int\limits_{0}^{1} \sin{\left(4 x + 3 \right)}\, dx$$

Integral(sin(4*x + 3), (x, 0, 1))

Detail solution

Let $u = 4 x + 3$ .

Then let $du = 4 dx$ and substitute $\frac{du}{4}$ :

$\int \frac{\sin{\left(u \right)}}{16}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{\sin{\left(u \right)}}{4}\, du = \frac{\int \sin{\left(u \right)}\, du}{4}$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(u \right)}\, du = - \cos{\left(u \right)}$
  So, the result is: $- \frac{\cos{\left(u \right)}}{4}$
Now substitute $u$ back in:

$- \frac{\cos{\left(4 x + 3 \right)}}{4}$
Now simplify:

$- \frac{\cos{\left(4 x + 3 \right)}}{4}$
Add the constant of integration:

$- \frac{\cos{\left(4 x + 3 \right)}}{4}+ \mathrm{constant}$

The answer is:

$- \frac{\cos{\left(4 x + 3 \right)}}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                  
 |                       cos(4*x + 3)
 | sin(4*x + 3) dx = C - ------------
 |                            4      
/

$$-{{\cos \left(4\,x+3\right)}\over{4}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

  cos(7)   cos(3)
- ------ + ------
    4        4

$${{\cos 3-\cos 7}\over{4}}$$

  cos(7)   cos(3)
- ------ + ------
    4        4

$$\frac{\cos{\left(3 \right)}}{4} - \frac{\cos{\left(7 \right)}}{4}$$

Упростить

Numerical answer [src]

-0.435973687735938

-0.435973687735938

The graph

Use the examples entering the upper and lower limits of integration.

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of sin(4x+3) dx

Limits of integration:

The graph:

Piecewise:

The solution