Primitive without solving

The expression of the function $h(x)$ that satisfies $\int\dfrac{e^{h(x)}}{2h(x)\sqrt{1-e^{2h(x)}}}dx=\arcsin(e^{\sqrt{x}})+C$ is:

# Integration calculus

Training
13

Integral by parts

Calculate $\displaystyle \int x~e^{-x}~dx$

# Integrals of functions

Training
13

Immediate integral

The primitive function of $\int x^2\tan(x^3)dx$ is:

# Integration calculus

Training
13

Primitive

Determine the value of $f(1)$, knowing that $f(0)=1$ and that $f^{\prime}(x)=\dfrac{4x}{(2-x^2)^3}$. (Enter the value with to 2 decimal places)

# Integrals of functions

Reasoning
13

Integral

Indicate the logical value $$\displaystyle \int \dfrac{1+x}{x^2+1}~dx=\arctan(x)+\ln|x^2+1|+ C$$

# Integrals of functions

Training
13

Integral

Calculate $\displaystyle \int \dfrac{1+x+x\sqrt{x^2+1}}{x^2+1}dx$

# Integrals of functions

Training
13