Integration by Parts Calculator

Integration is a process of finding the area covered below the graph of a function. There are different methods of integration and integration by parts is one of them. This method is usually applied to an integral of the functions which are multiplied together. Integration by parts calculator is the quick online tool which can easily find the integral of such functions.


Example 1: Find the integral of the function, f(x) = xcosx by using integration by parts.

Integral of the function f(x)  ∫xcosx dx

We can use integration by parts, since ‘x’ and ‘cosx’ are multiplied together.

Integration by parts formula  ∫u * vdv = uv - ∫v du

Let u = x   du = 1dx

Let vdv = cosx dx   ∫vdv = ∫cosx dx

v = sinx

Applying the integration by parts formula   ∫xcosx dx = (x*sinx) - ∫sinx dx

Hence  ∫xcosx dx = xsinx + cosx + c


 
Example 2: Find the integral of the function, f(x) = lnx by using integration by parts.

Integral of the function f(x)  ∫ lnx * 1dx

Integration by parts is the easiest method to find this integral and here ‘1’ and ‘lnx’ are multiplied together.

Integration by parts formula  ∫u * vdv = uv - ∫v du

Let u= lnx  du= 1/x dx

Let vdv = 1dx  ∫vdv= ∫1 dx

v = x

Applying the integration by parts formulaè∫ lnx dx = (x * lnx) - ∫x * 1/x dx

Hence ∫ lnx dx = xlnx – x + c