Primitive function

Indefinite Integrals

Submitted by michaela.bailova on Thu, 01/30/2025 - 16:18

Submitted by michaela.bailova on Thu, 01/30/2025 - 16:14

Submitted by michaela.bailova on Thu, 01/30/2025 - 15:31

Submitted by michaela.bailova on Sat, 11/30/2024 - 00:05

Submitted by michaela.bailova on Wed, 09/25/2024 - 14:26

Level:

Evaluate the following integral on the interval

(0; \frac{π}{2})

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

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

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

\sin 2 x - cotg 2 x - \ln 2 x + c; c \in R

\sin 2 x + cotg 2 x + \ln 2 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

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

(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 (\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