Answer to Question #198840 in Calculus for Muhammad Asif

Question

Evaluate the following indefinite integrals:  

a) ∫ (1/x + 3/x2 - 4/x3 ) dx

b) ∫ (x2 + 2x - 5) / √x dx

c) ∫ x ex dx

Answer 1

a)

$$\int(\dfrac{1}{x}+\dfrac{3}{x^2}-\dfrac{4}{x^3})dx$$

$$=\ln|x|-\dfrac{3}{x}+\dfrac{2}{x^2}+C$$

b)

$$\int\dfrac{x^2+2x-5}{\sqrt{x}}dx=\int( x^{3/2}+2x^{1/2}-5x^{-1/2})dx$$

$$={2 \over 5} x^{5/2}+{2 \over 3} x^{3/2}-10\sqrt{x}+C$$

c)

$$\int xe^xdx$$ $$\int udv=uv-\int vdu$$

$u=x, du=dx$

$dv=e^xdx, v=\int e^xdx=e^x$

$$\int xe^xdx=xe^x-\int e^xdx$$

$$=xe^x- e^xdx+C$$