Which of the following is the antiderivative f\left(x\right)=\sqrt{x}+\cos x?

\frac{2}{3}x^{\frac{3}{2}}+\sin x+C

What is the antiderivative: \frac{12x^5-6x^3+7}{2x}

\frac{6}{5}x^5-x^3+\frac{7}{2}\ln x+C

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Calculus Antiderivatives

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BASIC ANTIDERIVATIVES: includes introductions to antidifferentiation as a reverse process of differentiation, as well as antiderivatives of algebraic functions

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Questions 17

Answers

1
What is the antiderivative of f\left(x\right)=\csc^2x-e^x?
F\left(x\right)=\cot x+e^x+C
F\left(x\right)=\csc x+e^x+C
F\left(x\right)=\tan x-e^x+C
F\left(x\right)=-\cot x-e^x+C
2
What is the antiderivative of 2\sqrt{x}?
(x3/2 )/3 + c
- x-1/2 + c
(4x3/2)/ 3 + c
x3/2 + c
3
Find the specific antiderivative of f"(x)=40x³+20, f(1)=0, f'(1)=38
f(x)=2x5+10x2+38x+1
f(x)=2x5+10x2+8x-20
f(x)=40x3+10x2-102x+52
f(x)=40x3+10x2+38x+1
4
Find the specific antiderivative of f'(x)=8x³+12x, f(1)=10
f(x)=4x2+12x-6
f(x)=24x2+12x-26
f(x)=2x4+6x2+10
f(x)=2x4+6x2+2
5
What is the anti-derivative of x²?
(x2/2)+C
\frac{x^3}{3}+C
2x+C
x3+C
6
Which of the following is the antiderivative f\left(x\right)=\sqrt{x}+\cos x?
x^{\frac{3}{2}}-\sin x+C
\frac{2}{3}x^{\frac{3}{2}}+\sin x+C
\frac{x^{-\frac{1}{2}}}{2}-\sin x+C
\frac{1}{2\sqrt{x}}+\sin x+C
7
What is the anti-derivative of 2?
x2+C
C
0
2x+C
8
Find the antiderivative of \sin x\left(\cot x+\csc x\right)
\sin x\cot x+1
-\sin x+x+C
\sin x+x+C
\csc x+\cos x+C
9
Find the anti-derivative of x⁴+3x²+6
4x3+6x+C
-36
(x5/5)-x3-6x+C
(x5/5)+x3+6x+C
10
Find the anti-derivative of 1/x
ex+C
ln(x)
(1/x2)+C
ln∣x∣+C
11
f'\left(x\right)=3x^2-2;Find f\left(x\right) when f\left(1\right)=5
f\left(x\right)=x^3-2x+4
f\left(x\right)=x^3-2x+C
f\left(x\right)=3x^3-2x+6
f\left(x\right)=x^3-2x+6
12
Find the anti-derivative of cos(x)
-sin(x)+C
sin(x)+C
tan(x)+C
-cos(x)+C
13
What is the antiderivative? (3x + 4)(2x - 5)
2x3 - (7/2) x2 - 20x + c
(3/2 x2 + 4x) (x2 - 5x)
6x3 - 7x2 - 20 + c
2x3 - 7x2 - 20x + c
14
What is the antiderivative of \left(\sqrt{x}-1\right)\left(2\sqrt{x}+11\right)?
x2 + 3x3/2 - 11x + c
x2 + 6x3/2 - 11x
x2 + 6x3/2 - 11x + c
x2 + (27/2)x3/2 - 11x + c
15
What is the antiderivative of 5x⁴ - 2x + 1?
x5 - x2 + x
20x3 - 2
x5 - x2 + x + c
x5 - x2 + c
16
What is the antiderivative: \frac{12x^5-6x^3+7}{2x}
\frac{6}{5}x^5-x^3+C
6x4 - 3x2 +\frac{7}{2}x+ c
\frac{6}{5}x^5-x^3+\frac{7}{2}\ln x+C
x6- x3 +\frac{7}{2}x+ C
17
Find the anti-derivative of sec²(x)
sec(x)cot(x)+C
cot(x)+C
tan(x)+C
-tan(x)+C

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