Mister Exam

Other calculators

  • How to use it?

  • Integral of d{x}:
  • Integral of 1/(1+4x^2) Integral of 1/(1+4x^2)
  • Integral of 4*x*exp(x^2) Integral of 4*x*exp(x^2)
  • Integral of xln(1+x) Integral of xln(1+x)
  • Integral of sin^5 Integral of sin^5

  • Identical expressions

  • (seven *sin^3x+ five)/sin^2x
  • (7 multiply by sinus of cubed x plus 5) divide by sinus of squared x
  • (seven multiply by sinus of cubed x plus five) divide by sinus of squared x
  • (7*sin3x+5)/sin2x
  • 7*sin3x+5/sin2x
  • (7*sin³x+5)/sin²x
  • (7*sin to the power of 3x+5)/sin to the power of 2x
  • (7sin^3x+5)/sin^2x
  • (7sin3x+5)/sin2x
  • 7sin3x+5/sin2x
  • 7sin^3x+5/sin^2x
  • (7*sin^3x+5) divide by sin^2x
  • (7*sin^3x+5)/sin^2xdx

  • Similar expressions

  • (7*sin^3x-5)/sin^2x
Solving integrals/ (7*sin^3x+5)/sin^2x

Integral of (7*sin^3x+5)/sin^2x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |       3          
 |  7*sin (x) + 5   
 |  ------------- dx
 |        2         
 |     sin (x)      
 |                  
/                   
0
∫017sin⁡3(x)+5sin⁡2(x) dx\int\limits_{0}^{1} \frac{7 \sin^{3}{\left(x \right)} + 5}{\sin^{2}{\left(x \right)}}\, dx 
Integral((7*sin(x)^3 + 5)/sin(x)^2, (x, 0, 1))
Detail solution

  1. Rewrite the integrand:

    7sin⁡3(x)+5sin⁡2(x)=7sin⁡3(x)sin⁡2(x)+5sin⁡2(x)\frac{7 \sin^{3}{\left(x \right)} + 5}{\sin^{2}{\left(x \right)}} = \frac{7 \sin^{3}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{5}{\sin^{2}{\left(x \right)}}

  2. Integrate term-by-term:

    1. The integral of a constant times a function is the constant times the integral of the function:

      ∫7sin⁡3(x)sin⁡2(x) dx=7∫sin⁡3(x)sin⁡2(x) dx\int \frac{7 \sin^{3}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\, dx = 7 \int \frac{\sin^{3}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\, dx

      1. Don't know the steps in finding this integral.

        But the integral is

        −cos⁡(x)- \cos{\left(x \right)}

      So, the result is: −7cos⁡(x)- 7 \cos{\left(x \right)}

    1. The integral of a constant times a function is the constant times the integral of the function:

      ∫5sin⁡2(x) dx=5∫1sin⁡2(x) dx\int \frac{5}{\sin^{2}{\left(x \right)}}\, dx = 5 \int \frac{1}{\sin^{2}{\left(x \right)}}\, dx

      1. Don't know the steps in finding this integral.

        But the integral is

        −cos⁡(x)sin⁡(x)- \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}

      So, the result is: −5cos⁡(x)sin⁡(x)- \frac{5 \cos{\left(x \right)}}{\sin{\left(x \right)}}

    The result is: −7cos⁡(x)−5cos⁡(x)sin⁡(x)- 7 \cos{\left(x \right)} - \frac{5 \cos{\left(x \right)}}{\sin{\left(x \right)}}

  3. Now simplify:

    −7sin⁡(x)+5tan⁡(x)- \frac{7 \sin{\left(x \right)} + 5}{\tan{\left(x \right)}}

  4. Add the constant of integration:

    −7sin⁡(x)+5tan⁡(x)+constant- \frac{7 \sin{\left(x \right)} + 5}{\tan{\left(x \right)}}+ \mathrm{constant}

The answer is:

−7sin⁡(x)+5tan⁡(x)+constant- \frac{7 \sin{\left(x \right)} + 5}{\tan{\left(x \right)}}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                          
 |                                           
 |      3                                    
 | 7*sin (x) + 5                     5*cos(x)
 | ------------- dx = C - 7*cos(x) - --------
 |       2                            sin(x) 
 |    sin (x)                                
 |                                           
/
∫7sin⁡3(x)+5sin⁡2(x) dx=C−7cos⁡(x)−5cos⁡(x)sin⁡(x)\int \frac{7 \sin^{3}{\left(x \right)} + 5}{\sin^{2}{\left(x \right)}}\, dx = C - 7 \cos{\left(x \right)} - \frac{5 \cos{\left(x \right)}}{\sin{\left(x \right)}}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-10000000001000000000
Plot the graph f(x)
The answer [src] 
oo
∞\infty 
=
= 
oo
∞\infty 
oo
Numerical answer [src] 
6.89661838974298e+19
6.89661838974298e+19

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

    © Mister Exam – Calculator