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Antiderivatives and Indefinite Integrals

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Wize University Calculus 2 Textbook > Integration

Indefinite Integrals

4 Activities

Wize University Calculus 1 Textbook > Integrals

Antiderivatives & The Indefinite Integrals

5 Activities

Find the most general antiderivative of f(x)=e2f\left(x\right)=e^2
More Indefinite Integrals Questions:
Practice: Indefinite Integral
Find f(x)f\left(x\right), given that f′(x)=x2−2+sin⁡xf'\left(x\right)=x^2-2+\sin x and f(0)=3f\left(0\right)=3.
Practice: Indefinite Integral
Practice: Indefinite Integral
Find f(x)f\left(x\right), given that f′(x)=x2−2+sin⁡xf'\left(x\right)=x^2-2+\sin x and f(0)=3f\left(0\right)=3.
Practice: Indefinite Integral
Practice: Indefinite Integral
Find f(x)f\left(x\right), given that f′(x)=x2−2+sin⁡xf'\left(x\right)=x^2-2+\sin x and f(0)=3f\left(0\right)=3.
Indefinite Integrals: Trigonometric Functions
Evaluate the following indefinite integral
∫(sec⁡2x)(cos⁡22x)dx\displaystyle \int (\sec 2x)( \cos^2 2x)dx
Indefinite Integrals with Exponential
Compute the following integral: ∫3−x dx\displaystyle \int 3^{-x}\,\text{d}x.
Use upper case CC to denote any constants.
Antiderivatives: Indefinite integrals
Evaluate the integral ∫1+1x+2x2+3x3dx\displaystyle\int_{ }^{ }1+\frac{1}{x}+\frac{2}{x^2}+\frac{3}{x^3}dx.
Indefinite Integrals
Evaluate the following indefinite integral
∫x4−3xxdx\displaystyle \int \frac{x^4-3x}{x}dx
Antiderivatives: Indefinite integrals
Evaluate the indefinite integral ∫x23−x5+1x34dx\displaystyle \int \sqrt[3]{x^2}-\sqrt[5]{x}+\frac{1}{\sqrt[4]{x^3}}dx.
More Antiderivatives & The Indefinite Integrals Questions:
Practice: Definite Integral
Practice: Definite Integral
Evaluate ∫−20∣x2−1∣dx\displaystyle \int_{-2}^0\left|x^2-1\right|dx.
Antiderivatives: Indefinite integrals
Evaluate the integral ∫1+1x+2x2+3x3dx\displaystyle\int_{ }^{ }1+\frac{1}{x}+\frac{2}{x^2}+\frac{3}{x^3}dx.
Antiderivatives: Indefinite integrals
Evaluate the integral ∫1+1x+2x2+3x3dx\displaystyle\int_{ }^{ }1+\frac{1}{x}+\frac{2}{x^2}+\frac{3}{x^3}dx.
Antiderivatives: Indefinite Integrals
If F(x)=ln⁡(2x2)F(x) = \ln(2x^2) is an antiderivative of f(x)f(x), find ff.
Practice: Definite Integral
Practice: Definite Integral
Evaluate ∫−20∣x2−1∣dx\displaystyle \int_{-2}^0\left|x^2-1\right|dx.
Find ∫(x23−x5+1x34)dx\displaystyle \int \left(\sqrt[3]{x^2}-\sqrt[5]{x}+\frac{1}{\sqrt[4]{x^3}}\right)dx
Practice: Indefinite Simplify First
Q:\textbf{Q:} Find ∫[x2−4xx+x(2x2−3x)]dx\displaystyle\int_{ }^{ }\left[\frac{x^2-4\sqrt{x}}{\sqrt{x}}+x\left(2x^2-3x\right)\right]dx
Practice: Indefinite Integral
Evaluate the integral ∫x+1+1x+2x2dx\displaystyle\int_{ }^{ }x+1+\frac{1}{x}+\frac{2}{x^2}dx
Practice: Indefinite Integral
Evaluate the integral ∫1+1x+2x2+3x3dx\displaystyle\int_{ }^{ }1+\frac{1}{x}+\frac{2}{x^2}+\frac{3}{x^3}dx.
Antiderivatives: Exponential Functions
Which of the following is the most general antiderivative of the function e3x+7e^{3x+7}? In the functions below, cc is an arbitrary constant.
Riemann Sums
Evaluate lim⁡n→∞ ∑i=1n[5n[(1+5in)2−3]]\displaystyle \lim_{n\to\infty}\ \sum_{i=1}^n\left[\frac{5}{n}\left[\left(1+\frac{5i}{n}\right)^2-3\right]\right]
Find ∫xe3 dx\int_{ }^{ }xe^3\ dx
Antiderivatives: Indefinite Integrals
If F(x)=ln⁡(2x2)F(x) = \ln(2x^2) is an antiderivative of f(x)f(x), find ff.
Antiderivatives: Indefinite Integrals
The graph of an antiderivative of f(x)f(x) is given below. Graph f(x)f(x).
Find an antiderivative for
f(x)=x5+2x4x\displaystyle f(x)=\frac{x^5+2\sqrt{x}}{4x}
Find an antiderivative for
f(x)=x5+2x4x\displaystyle f(x)=\frac{x^5+2\sqrt{x}}{4x}
Find ∫ln(e4x)dx\displaystyle \int ln(e^{4x})dx
If F(x)=ln⁡(2x2)F(x)=\ln(2x^2) is an antiderivative of f(x)f(x), find f.
Antiderivatives: Indefinite integrals
Evaluate the integral ∫1+1x+2x2+3x3dx\displaystyle\int_{ }^{ }1+\frac{1}{x}+\frac{2}{x^2}+\frac{3}{x^3}dx.
Practice: Indefinite Simplify First
Q:\textbf{Q:} Find ∫[x2−4xx+x(2x2−3x)]dx\displaystyle\int_{ }^{ }\left[\frac{x^2-4\sqrt{x}}{\sqrt{x}}+x\left(2x^2-3x\right)\right]dx
Find ∫(x23−x5+1x34)dx\displaystyle \int \left(\sqrt[3]{x^2}-\sqrt[5]{x}+\frac{1}{\sqrt[4]{x^3}}\right)dx
Antiderivatives: Indefinite integrals
Evaluate the indefinite integral ∫x23−x5+1x34dx\displaystyle \int \sqrt[3]{x^2}-\sqrt[5]{x}+\frac{1}{\sqrt[4]{x^3}}dx.
Indefinite Integrals: Antiderivatives
Find the indefinite integral ∫2x(2x+3)2dx\int2x(2x+3)^2dx
Find ∫xe3 dx\int_{ }^{ }xe^3\ dx
Antiderivatives: Indefinite Integrals
Find ∫[x2−4xx+x(2x2−3x)]dx\int_{ }^{ }\left[\frac{x^2-4\sqrt{x}}{\sqrt{x}}+x\left(2x^2-3x\right)\right]dx.
Practice: Definite Integral
Practice: Definite Integral
Evaluate ∫−20∣x2−1∣dx\displaystyle \int_{-2}^0\left|x^2-1\right|dx.
Antiderivatives: Indefinite Integrals
For the following function, find the most general antiderivative.
f(x)=x5+2x4x\displaystyle f(x)=\frac{x^5+2\sqrt{x}}{4x}
Find the antiderivative FF
f(x)=4x+x22+5,F(1)=1/3\displaystyle f(x)=4x+\frac{x^2}{2}+5, F(1)=1/3