Integration by parts Problems and solutions

The integration by parts is a mathematical process of finding the integral of the product of functions by expressing it in terms of the product of their derivative and antiderivative. Here is a worksheet on the integration by parts for your practice and solutions to learn how to use the integration by parts as a formula in calculating both indefinite and definite integrals of the product of functions.

Indefinite integration

$(1).\,\,$ Evaluate $\displaystyle \int{xe^x}\,dx$

$(2).\,\,$ Evaluate $\displaystyle \int{\log_{e}{x}}\,dx$

$(3).\,\,$ Evaluate $\displaystyle \int{\dfrac{x-\sin{x}}{1-\cos{x}}}\,dx$

$(4).\,\,$ Evaluate $\displaystyle \int{\sin{\sqrt{x}}}\,dx$

The list of indefinite integral questions on integration by parts with solutions to learn how to find the indefinite integrals of the product of functions.

Definite integration

$(1).\,\,$ Evaluate $\displaystyle \int_{0}^{\Large \frac{\pi}{2}}{x\cos{x}}\,dx$

$(2).\,\,$ Evaluate $\displaystyle \int_{0}^{1}{e^{\displaystyle x^2}.x^3}\,dx$

$(3).\,\,$ Evaluate $\displaystyle \int_{0}^{\Large \frac{\pi}{4}}{x\sec^2{x}}\,dx$

The list of definite integral problems on integration by parts with solutions to learn how to evaluate the definite integrals of the product of functions.

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