Primitive function

2010001507

Level:

Evaluate the following integral on the interval

(0; + \infty)

\int \frac{19 \sqrt[3]{x^{4}} - 3}{\sqrt[4]{x^{3}}} d x

12 (x \sqrt[12]{x^{7}} - \sqrt[4]{x}) + c, c \in R

\frac{\frac{57}{7} \sqrt[3]{x^{7}} - 3 x}{\frac{4}{7} \sqrt[4]{x^{7}}} + c, c \in R

\frac{361}{12} \sqrt[12]{x^{19}} - \frac{3}{4} \sqrt[4]{x} + c, c \in R

Level:

Evaluate the following integral on the interval

(0; + \infty)

\int (\frac{1}{\sqrt{x}} + \frac{2}{x} + \frac{3}{x^{2}}) d x

2 \sqrt{x} + 2 \ln x - \frac{3}{x} + c; c \in R

\frac{3}{2 \sqrt{x^{3}}} + \frac{4}{x^{2}} + \frac{9}{x^{3}} + c; c \in R

\frac{2}{3 \sqrt{x^{3}}} + \frac{1}{x^{2}} + \frac{1}{x^{3}} + c; c \in R

\frac{\sqrt{x}}{2} + 2 \ln x - \frac{3}{x} + c; c \in R

Level:

Evaluate the following integral on the interval

(0; + \infty)

\int (\frac{1}{x} - \frac{2}{x^{2}} + \frac{3}{\sqrt{x}}) d x

\ln x + \frac{2}{x} + 6 \sqrt{x} + c; c \in R

\frac{2}{x^{2}} - \frac{6}{x^{3}} + \frac{9}{2 \sqrt{x^{3}}} + c; c \in R

\frac{1}{2 x^{2}} - \frac{2}{3 x^{3}} + \frac{2}{\sqrt{x^{3}}} + c; c \in R

\ln x + \frac{2}{x} + \frac{3 \sqrt{x}}{2} + c; c \in R

Level:

Evaluate the following integral on

R

\int (x^{2} + 2 \sin^{2} x + 3 e^{2 x}) d x

\frac{x^{3}}{3} + x - \sin x \cos x + \frac{3}{2} e^{2 x} + c; c \in R

3 x^{3} + x - \sin x \cos x + 6 e^{2 x} + c; c \in R

\frac{x^{3}}{3} + \frac{2}{3} \sin^{3} x + e^{3 x} + c; c \in R

\frac{x^{3}}{3} - 2 \cos^{2} x + 3 e^{2 x} + c; c \in R

Level:

Evaluate the following integral on

R

\int (3 x^{3} + e^{2 x} - \cos^{2} x) d x

\frac{3 x^{4}}{4} + \frac{e^{2 x}}{2} - \frac{x}{2} - \frac{1}{2} \sin x \cos x + c; c \in R

12 x^{4} + 2 e^{2 x} - \frac{x}{2} - \frac{1}{2} \sin x \cos x + c; c \in R

\frac{3 x^{4}}{4} + \frac{e^{3 x}}{3} - \frac{1}{3} \cos^{3} x + c; c \in R

\frac{3 x^{4}}{4} + e^{2 x} - \sin^{2} x + c; c \in R

Level:

Evaluate the following integral on the interval

(0; + \infty)

\int (\frac{1}{x} + \frac{1}{x + 1} + \frac{x}{x^{2} + 2}) d x

\ln x + \ln (x + 1) + \frac{1}{2} \ln (x^{2} + 2) + c; c \in R

\ln x + \ln (x + 1) + \frac{1}{2} x^{2} \ln (x^{2} + 2) + c; c \in R

\frac{2}{x^{2}} + \frac{1}{\frac{1}{2} x^{2} + x} + \frac{\frac{1}{2} x^{2}}{\frac{1}{3} x^{3} + 2 x} + c; c \in R

\ln x + \ln (x + 1) + \frac{3 x}{2 (x^{2} + 6)} + c; c \in R

Level:

Evaluate the following integral on the interval

(0; + \infty)

\int (\frac{2}{x} + \frac{1}{x + 2} + \frac{x}{x^{2} + 1}) d x

2 \ln x + \ln (x + 2) + \frac{1}{2} \ln (x^{2} + 1) + c; c \in R

2 \ln x + \ln (x + 2) + \frac{1}{2} x^{2} \ln (x^{2} + 1) + c; c \in R

\frac{4}{x^{2}} + \frac{1}{\frac{1}{2} x^{2} + 2 x} + \frac{\frac{1}{2} x^{2}}{\frac{1}{3} x^{3} + x} + c; c \in R

2 \ln x + \ln (x + 2) + \frac{3 x}{2 (x^{2} + 3)} + c; c \in R

Level:

Evaluate the following integral on the interval

(0; + \infty)

\int (x \sqrt{x} + x \cos x - x e^{x}) d x

\frac{2}{5} x^{2} \sqrt{x} + x \sin x + \cos x - x e^{x} + e^{x} + c; c \in R

\frac{x^{2}}{2} (\frac{2}{3} x^{\frac{3}{2}} + \sin x - e^{x}) + c; c \in R

\frac{2}{5} x^{2} \sqrt{x} + x \sin x - \cos x - x e^{x} + e^{x} + c; c \in R

\frac{2}{5} x^{2} \sqrt{x} + x \sin x + \cos x - x e^{x} - e^{x} + c; c \in R

Level:

Evaluate the following integral on the interval

(0; + \infty)

\int (x \sqrt[3]{x} + x \sin x + x e^{x}) d x

\frac{3}{7} x^{2} \sqrt[3]{x} + x \cos x + \sin x + x e^{x} - e^{x} + c; c \in R

\frac{x^{2}}{2} (\frac{3}{4} x^{\frac{4}{3}} - \cos x + e^{x}) + c; c \in R

\frac{3}{7} x^{2} \sqrt[3]{x} + x \cos x - \sin x + x e^{x} - e^{x} + c; c \in R

\frac{3}{7} x^{2} \sqrt[3]{x} - x \cos x + \sin x + x e^{x} + e^{x} + c; c \in R

Level:

Evaluate the following integral on the interval

(\frac{π}{4}; \frac{3 π}{4})

\int (\frac{1}{2 x} + \sin 2 x - \frac{1}{\cos^{2} 2 x}) d x

\frac{1}{2} (\ln x - \cos 2 x - tg 2 x) + c; c \in R

\frac{1}{2} (\ln (2 x) - \cos 2 x - tg 2 x) + c; c \in R

\ln (2 x) - \cos 2 x - tg 2 x + c; c \in R

\ln (2 x) + \cos 2 x - cotg 2 x + c; c \in R