Primitive function

2010000306

Level:

Evaluate the following integral on the interval

(0; + \infty)

\int x^{3} \ln x d x

\frac{x^{4}}{4} \ln x - \frac{x^{4}}{16} + c, c \in R

\frac{x^{3}}{3} \ln x - \frac{x^{3}}{9} + c, c \in R

\frac{x^{2}}{2} \ln x - \frac{x^{2}}{4} + c, c \in R

x \ln x - x + c, c \in R

Level:

Evaluate the following integral on

R

\int \sin^{2} x \cos x d x

\frac{\sin^{3} x}{3} + c, c \in R

- \frac{\cos^{3} x \sin x}{3} + c, c \in R

2 \sin x + c, c \in R

Level:

Identify the formula for integration by parts.

\int u (x) v^{'} (x) d x = u (x) v (x) - \int u^{'} (x) v (x) d x

\int u (x) v (x) d x = u^{'} (x) v^{'} (x) - \int u^{'} (x) v (x) d x

\int u^{'} (x) v^{'} (x) d x = u (x) v (x) - \int u^{'} (x) v (x) d x

\int u (x) v^{'} (x) d x = u (x) v (x) + \int u^{'} (x) v (x) d x

Level:

Evaluate the following integral on

R

\int x^{2} \sin x d x

- x^{2} \cos x + 2 x \sin x + 2 \cos x + c, c \in R

x^{2} \cos x - 2 x \sin x - 2 \cos x + c, c \in R

\frac{1}{3} x^{3} \cos x + c, c \in R

\frac{1}{3} x^{3} - \cos x + c, c \in R

Level:

Evaluate the following integral on the interval

(0; + \infty)

\int \ln x d x

x \ln x - x + c, c \in R

\ln x - x + c, c \in R

x \ln x + x + c, c \in R

x \ln x - \frac{1}{2} x^{2} + c, c \in R

Level:

Evaluate the following integral on the interval

(0; + \infty)

\int x \ln x d x

\frac{1}{2} x^{2} \ln x - \frac{1}{4} x^{2} + c, c \in R

x \ln x - \frac{1}{2} x^{2} + c, c \in R

x \ln x - x + c, c \in R

\frac{1}{2} x^{2} + \frac{1}{| x |} + c, c \in R

Level:

Evaluate the following integral on the interval

(0; + \infty)

\int x^{2} \ln x d x

\frac{1}{3} x^{3} \ln x - \frac{1}{9} x^{3} + c, c \in R

\frac{1}{2} x^{2} \ln x - \frac{1}{4} x^{2} + c, c \in R

x \ln x - \frac{1}{2} x^{2} + c, c \in R

x \ln x - x + c, c \in R

Level:

Evaluate the following integral on

R

\int x^{2} e^{x} d x

x^{2} e^{x} - 2 x e^{x} + 2 e^{x} + c, c \in R

x^{2} e^{x} + 2 x e^{x} - 2 e^{x} + c, c \in R

\frac{1}{3} x^{3} e^{x} - \frac{1}{2} x^{2} e^{x} + 2 e^{x} + c, c \in R

\frac{1}{3} x^{3} e^{x} + \frac{1}{2} x^{2} e^{x} - 2 e^{x} + c, c \in R

Level:

Evaluate the following integral on

R

\int e^{2 x} d x

\frac{1}{2} e^{2 x} + c, c \in R

\frac{1}{3} e^{3 x} + c, c \in R

e^{2 x} - e^{x} + c, c \in R

2 e^{2 x} + c, c \in R

Level:

Evaluate the following integral on the interval

(0; + \infty)

\int x^{2} \ln x d x

\frac{x^{3}}{3} (\ln x - \frac{1}{3}) + c, c \in R

\frac{x^{2}}{3} + c, c \in R

x^{2} (\frac{x \ln x}{3} - \frac{1}{2}) + c, c \in R