Primitive function

1003018701

Level:

Evaluate the following integral on

(0; π)

\int (π e^{x} - \frac{3}{\sin^{2} x}) d x

π e^{x} + 3 cotg x + c, c \in R

π e^{x} + 3 tg x + c, c \in R

π e^{x} + cotg x + c, c \in R

π e^{x} - 3 cotg x + c, c \in R

1003018702

Level:

Evaluate the following integral on

R

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

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

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

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

9 x + 6 x + \frac{3^{x}}{\ln 3} - e^{x} + 2^{e} x + c, c \in R

1003018703

Level:

Evaluate the following integral on

(\frac{π}{2}; π)

\int (7 \cos x + \frac{5}{\cos^{2} x} + \frac{3}{\sin^{2} x}) d x

7 \sin x + 5 tg x - 3 cotg x + c, c \in R

- 7 \sin x + 5 tg x + 3 cotg x + c, c \in R

- 7 \sin x - 5 tg x - 3 cotg x + c, c \in R

7 \sin x - 5 tg x + 3 cotg x + c, c \in R

1003018704

Level:

Evaluate the following integral on

(0; \infty)

\int (3 \sqrt{x} + 4 \sqrt[3]{x} - 35 \sqrt[4]{x^{3}}) d x

2 x \sqrt{x} + 3 x \sqrt[3]{x} - 20 x \sqrt[4]{x^{3}} + c, c \in R

\frac{9}{2} x \sqrt{x} + \frac{16}{3} x \sqrt[3]{x} - \frac{245}{4} x \sqrt[4]{x^{3}} + c, c \in R

2 \sqrt{x} + 3 \sqrt[3]{x} - 20 \sqrt[4]{x^{3}} + c, c \in R

2 \sqrt[3]{x} + 3 \sqrt[4]{x^{3}} - 20 \sqrt[7]{x^{4}} + c, c \in R

1003018705

Level:

Evaluate the following integral on

(0; \infty)

\int (3 \sqrt{x^{7}} - \sqrt[5]{x^{4}}) d x

\frac{2}{3} x^{4} \sqrt{x} - \frac{5}{9} x \sqrt[5]{x^{4}} + c, c \in R

\frac{3}{2} x^{4} \sqrt{x} - \frac{9}{5} x \sqrt[5]{x^{4}} + c, c \in R

\frac{2}{9} x^{4} \sqrt{x} - \frac{5}{9} x \sqrt[5]{x^{4}} + c, c \in R

\frac{2}{3} \sqrt[9]{x^{2}} - \frac{5}{9} \sqrt[9]{x^{5}} + c, c \in R

1003018706

Level:

Evaluate the following integral on

(0; \infty)

\int (\frac{5}{x} - \frac{x}{5}) d x

5 \ln | x | - \frac{x^{2}}{10} + c, c \in R

5 x^{0} + \frac{1}{10} x^{2} + c, c \in R

5 \ln x + \frac{x^{2}}{10} + c, c \in R

\ln | x | + \frac{x^{2}}{5} + c, c \in R

1003018707

Level:

Given the function

F (x) = \frac{2}{3} \cos x - \frac{x^{2}}{2} \cdot \ln 4

, find the function

f

such that

F

is primitive to

f

R

f (x) = - \frac{2}{3} \sin x - x \ln 4

f (x) = \frac{2}{3} \sin x - x \ln 4

f (x) = \frac{2}{3} \sin x - 2 x \ln 2

f (x) = - \frac{2}{3} \sin x - 2 x

1003018708

Level:

Given the function

F (x) = 5 e^{x} + 2 \sqrt{x}

, find the function

f

such that

F

is primitive to

f

(0; \infty)

f (x) = 5 e^{x} + \frac{\sqrt{x}}{x}

f (x) = 5 e^{x} + \sqrt{x}

f (x) = e^{x} + \frac{\sqrt{x}}{x}

f (x) = 5 e^{x} - \frac{\sqrt{x}}{x}

1003018709

Level:

Four children evaluated the following integral

I

R

. Who made a mistake?

I = \int (5 x^{4} + 9 x^{2} - 6 x) d x

Paul:

I = (x^{3} + 3) \cdot x^{2} - 3 x^{3} + c, c \in R

Jane:

I = x^{2} (x^{3} + 3 x - 3) + c, c \in R

Ann:

I = x^{5} + 3 x^{3} - 3 x^{2} + c, c \in R

Miky:

I = x^{5} + (3 x - 3) \cdot x^{2} + c, c \in R

1003018710

Level:

Four children evaluated the following integral

I

(0; \infty)

. Who made a mistake?

I = \int (\frac{1}{8} \sqrt[8]{x^{3}} + \frac{1}{2} \sqrt{x^{9}} - \frac{1}{5} \sqrt[5]{x^{6}}) d x

Paul:

I = \frac{1}{11} (x^{3} \sqrt[8]{x} + x \sqrt{x^{5}} - x \sqrt[5]{x^{2}}) + c, c \in R

Jane:

I = \frac{1}{11} (x \sqrt[8]{x^{3}} + x^{5} \sqrt{x} - x^{2} \sqrt[5]{x} + c), c \in R

Ann:

I = \frac{1}{11} (x \sqrt[8]{x^{3}} + x^{5} \sqrt{x} - x^{2} \sqrt[5]{x}) + c, c \in R

Miky:

I = \frac{x}{11} \sqrt[8]{x^{3}} + \frac{x^{5}}{11} \sqrt{x} - \frac{x^{2}}{11} \sqrt[5]{x} + c, c \in R

1003018701

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