Algebraic Indefinite integration Problems and Solutions

In indefinite integration, the algebraic functions are involved. For calculating the indefinite integrals of the algebraic functions, it is important to learn the integral rules of the algebraic functions firstly. The following is the list of indefinite integral problems with solutions to learn how to evaluate the indefinite integration of the algebraic functions by using the integration formulas.

Exponential functions

Evaluate $\displaystyle \int{xe^x \,} dx$

Rational functions

Evaluate $\displaystyle \int{\dfrac{1}{x^2+6x+10}\,\,}dx$

Evaluate $\displaystyle \int{\dfrac{1}{x^2+4x+3} \,} dx$

Irrational functions

Evaluate $\displaystyle \int{\dfrac{1}{x^{\frac{1}{2}}(2+3x)^{\frac{3}{2}}}\,}dx$

Evaluate $\displaystyle \int{\dfrac{x}{(x^2+2x+2)\sqrt{x+1}}\,}dx$

Evaluate $\displaystyle \int{\dfrac{1}{(2+3x^2)^\frac{3}{2}}\,}dx$