# INTEGRATION BY PARTS WORKSHEET

## About "Integration by Parts Worksheet"

Integration by Parts Worksheet :

Here we are going to see some practice questions using the concept "Integration by parts".

Integration by parts method is generally used to find the integral when the integrand is a product of two different types of functions or a single logarithmic function or a single inverse trigonometric function or a function which is not integrable directly.

Formula :

∫udv  =  uv - ∫vdu

By differentiating "u" we get "du", by integrating dv we get v.

## Integration by Parts  - Practice questions

(1)  Integrate the following with respect to x:

9xe3x              Solution

(2)  Integrate the following with respect to x:

x sin 3x              Solution

(3)  Integrate the following with respect to x:

25 xe-5x               Solution

(4)  Integrate the following with respect to x:

x sec x tan x             Solution

(5)  Integrate the following with respect to x:

x log x           Solution

(6)  Integrate the following with respect to x:

27x2 e3x           Solution

(7)  Integrate the following with respect to x:

x2 cos x           Solution

(8)  Integrate the following with respect to x:

x3 sin x           Solution

(9)  Integrate the following with respect to x:

x sin-1x /√(1-x2)          Solution

(10)  Integrate the following with respect to x:

x5 e^x2

(11)  Integrate the following with respect to x:

tan-1 (8x /1 - 16x2)

(12)  Integrate the following with respect to x:

sin-1 (2x /1 + x2)

After having gone through the stuff given above, we hope that the students would have understood, "Integration by Parts Worksheet"

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