The integral of sinxcosx is equal to -(cos2x)/4+C or, (sin^{2}x)/2+C where C is an integration constant. In this post, we will learn how to integrate sinx cosx.

The integration formula of sinxcosx is give as follows:

- ∫sinx cosx dx = -(cos2x)/4+C
- ∫sinx cosx dx = (sin
^{2}x)/2+C. - ∫sinx cosx dx = -(cos
^{2}x)/2+C.

## Find the integration of sinx cosx

**Answer: **The integration of sinx cosx is (sin^{2}x)/2+C.

*proof:*

There are three methods to find the integration of sinx cosx which we will discuss now. They are the substitutions of sinx, cosx and the formula of sin2x.

## Integration of Sinx Cosx by Substituting Sinx

The given integral is ∫sinx cosx dx

Put sinx = z.

So we have cosx dx = dz. Now, substituting these values in the given integral we obtain that

∫sinx cosx dx

= ∫z dz

= z^{2}/2+C by the power rule of integration ∫x^{n}dx = x^{n+1}/(n+1).

= sin^{2}x/2+C

So the integration of sinxcosx is (sin^{2}x)/2+C where C denotes the constant of integrals.

## Integration of Sinx Cosx by Substituting Cosx

∫sinx cosx dx

Put cosx = t.

So -sinx dx = dt. Therefore, we obtain that

∫sinx cosx dx = -∫z dz

= -z^{2}/2+C by the rule ∫x^{n}dx = x^{n+1}/(n+1).

= -cos^{2}x/2+C

So the integration of sinxcosx is -(cos^{2}x)/2+C.

**ALSO READ:**

By the trigonometric formula sin2x = 2sinx cosx, we can write the function sinxcosx as follows:

sinxcosx = (sin2x)/2.

Now, integrating we will get that

∫sinx cosx dx = ∫(sin2x)/2 dx

= 1/2 × ∫sin2x dx

= -1/2 × (cos2x)/2 + C as we know that ∫sin2x dx = -(cosmx)/m.

= -(cos2x)/4+C.

So the integral of sinx cosx is equal to -(cos2x)/4+C.

Have You Read These Integrations?

Integration of root(x) + 1/root(x)

## FAQs

**Q1: What is the integration of sinxcosx?**

Answer: The integration of sinxcosx is given by ∫sinx cosx dx = -(cos2x)/4+C where C is an integral constant.