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1003107904

Level:

Solve the indefinite integral

\int (a b e^{c} - b x^{2} + 5^{b} - \sin c) d b

of a real-valued function, where

x

a

c

are real numbers.

0.5 a e^{c} b^{2} - \frac{b^{2}}{2} x^{2} + \frac{5^{b}}{\ln 5} - b \sin c + k

k \in R

0.5 a e^{c} b^{2} - \frac{b^{2}}{2} \cdot \frac{x^{3}}{3} + \frac{5^{b}}{\ln 5} - b \sin c + k

k \in R

a e^{c} - 2 b x + 5^{b} - \sin c + k

k \in R

a e^{c} - b x^{2} + 5^{b} - b \sin c + k

k \in R

1003107903

Level:

Solve the indefinite integral

\int (a b e^{c} - b x^{2} + 5^{b} - \sin c) d a

of a real-valued function, where

x

b

c

are real numbers.

\frac{a^{2} b e^{c}}{2} - a b x^{2} + a 5^{b} - a \sin c + k

k \in R

\frac{a^{2}}{2} b e^{c} + k

k \in R

b e^{c} - b x^{2} + 5^{b} - \sin c + k

k \in R

a b e^{c} - b \frac{x^{3}}{3} + k

k \in R

1003107902

Level:

Solve the indefinite integral

\int (a b e^{c} - b x^{2} + 5^{b} - \sin c) d x

of a real-valued function, where

a

b

c

are real numbers.

a b e^{c} x - b \frac{x^{3}}{3} + 5^{b} x - x \sin c + k

k \in R

- b \frac{x^{3}}{3} + k

k \in R

a b e^{c} - 2 b + 5^{b} - \sin c + k

k \in R

a b e^{c} x - 2 b x + 5^{b} x - x \sin c + k

k \in R

1003107901

Level:

Solve the indefinite integral

\int \sin^{3} x \cos^{2} x d x

of a real-valued function using a suitable substitution.

\frac{\cos^{5} x}{5} - \frac{\cos^{3} x}{3} + c

- \frac{\cos^{5} x}{5} + \frac{\cos^{3} x}{3} + c

\frac{\cos^{5} x}{5} + \frac{\cos^{3} x}{3} + c

- \frac{\cos^{5} x}{5} - \frac{\cos^{3} x}{3} + c

1003164005

Level:

Evaluate the expression

\sqrt[3]{\sqrt[3]{10} - \sqrt[3]{2}} \cdot \sqrt[3]{\sqrt[3]{100} + \sqrt[3]{20} + \sqrt[3]{4}} .

2

8

\sqrt[3]{10} - \sqrt[3]{2}

\sqrt[3]{100} - \sqrt[3]{4}

1003164004

Level:

Evaluate the expression

\frac{5 x^{2} + 10 x + 10}{(x + 1)^{4} - 1}

for

x = \sqrt{5} - 2

and write the result in the form

a + b \sqrt{c}

, where

a

b

c

are natural numbers.

5 + 2 \sqrt{5}

2 + 5 \sqrt{2}

5 + 5 \sqrt{2}

5 + 5 \sqrt{5}

1003164003

Level:

Let

a = {[{(2 - \sqrt{3})}^{\frac{1}{2}} + {(2 + \sqrt{3})}^{\frac{1}{2}}]}^{2}, b = \frac{81^{- 1} \cdot \sqrt{3}}{27^{- 2} \cdot \sqrt[4]{9}} .

Comparing the numbers

a^{b}

and

b^{a}

you get:

a^{b} > b^{a}

a^{b} < b^{a}

a^{b} \leq b^{a}

a^{b} = b^{a}

1003164002

Level:

After simplifying the expression

a = \sqrt{6 - 2 \sqrt{5}} - \sqrt{5}

we get:

- 1

6 - \sqrt{5}

6 + \sqrt{5}

1 - 2 \sqrt{5}

1003164001

Level:

After simplifying the expression

\sqrt[3]{5 \sqrt{2} + 7} - \sqrt[3]{5 \sqrt{2} - 7}

we get:

2

2 \sqrt[3]{57}

1

2 \sqrt[3]{97}

1003158507

Level:

Let there be a row of five yellow cubes lying side by side. The first cube has an edge length of

100 cm

and each next cube has an edge length by

10 cm

shorter than the previous one. Let there be a second row of five blue cubes lying side by side. The first blue cube has an edge length of

100 cm

and each next cube has an edge length by

10 %

smaller than the previous one. What is the difference between the length of these two rows?

9.51 cm

34.51 cm

0 cm

20 cm

20.51 cm

C

1003107904

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